diff --git a/src/bin/sage-fixdoctests b/src/bin/sage-fixdoctests
index 49de702cd51..0d55581c505 100755
--- a/src/bin/sage-fixdoctests
+++ b/src/bin/sage-fixdoctests
@@ -300,6 +300,9 @@ def process_block(block, src_in_lines, file_optional_tags, venv_explainer=''):
         got = ['']
     else:
         expected, got = block.split('\nGot:\n')
+        got = re.sub(r'(doctest:warning).*^( *DeprecationWarning:)',
+                     r'\1...\n\2',
+                     got, 1, re.DOTALL | re.MULTILINE)
         got = got.splitlines()      # got can't be the empty string
 
     if args.only_tags:
diff --git a/src/sage/categories/schemes.py b/src/sage/categories/schemes.py
index 0d62237a636..cb1133a2192 100644
--- a/src/sage/categories/schemes.py
+++ b/src/sage/categories/schemes.py
@@ -139,8 +139,8 @@ def _call_(self, x):
                       To:   Rational Field
 
         """
-        from sage.schemes.generic.scheme import is_Scheme
-        if is_Scheme(x):
+        from sage.schemes.generic.scheme import Scheme
+        if isinstance(x, Scheme):
             return x
         from sage.schemes.generic.morphism import is_SchemeMorphism
         if is_SchemeMorphism(x):
@@ -197,9 +197,9 @@ def _repr_object_names(self):
             sage: Schemes(Spec(ZZ)) # indirect doctest
             Category of schemes over Integer Ring
         """
-        from sage.schemes.generic.scheme import is_AffineScheme
+        from sage.schemes.generic.scheme import AffineScheme
         base = self.base()
-        if is_AffineScheme(base):
+        if isinstance(base, AffineScheme):
             base = base.coordinate_ring()
         return f"schemes over {base}"
 
@@ -228,8 +228,8 @@ def __init__(self, base):
             sage: AbelianVarieties(Spec(QQ))
             Category of abelian varieties over Rational Field
         """
-        from sage.schemes.generic.scheme import is_AffineScheme
-        if is_AffineScheme(base):
+        from sage.schemes.generic.scheme import AffineScheme
+        if isinstance(base, AffineScheme):
             base = base.coordinate_ring()
         if base not in Fields():
             raise ValueError('category of abelian varieties is only defined over fields')
@@ -331,8 +331,8 @@ def __init__(self, base):
             sage: Jacobians(Spec(QQ))
             Category of Jacobians over Rational Field
         """
-        from sage.schemes.generic.scheme import is_AffineScheme
-        if is_AffineScheme(base):
+        from sage.schemes.generic.scheme import AffineScheme
+        if isinstance(base, AffineScheme):
             base = base.coordinate_ring()
         if base not in Fields():
             raise ValueError('category of Jacobians is only defined over fields')
diff --git a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
index 6938068bbc6..a1e4bc1700d 100644
--- a/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/affine_ds.py
@@ -50,7 +50,7 @@ class initialization directly.
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space_field
 from sage.schemes.affine.affine_morphism import SchemeMorphism_polynomial_affine_space_finite_field
-from sage.schemes.affine.affine_space import is_AffineSpace
+from sage.schemes.affine.affine_space import AffineSpace_generic
 from sage.schemes.affine.affine_space import AffineSpace
 from sage.schemes.affine.affine_subscheme import AlgebraicScheme_subscheme_affine
 from sage.schemes.generic.morphism import SchemeMorphism_polynomial
@@ -246,7 +246,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
             R = morphism.base_ring()
             polys = list(morphism)
             domain = morphism.domain()
-            if not is_AffineSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
+            if not isinstance(domain, AffineSpace_generic) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
                 raise ValueError('"domain" must be an affine scheme')
             if domain != morphism_or_polys.codomain():
                 raise ValueError('domain and codomain do not agree')
@@ -295,7 +295,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None):
         R = domain.base_ring()
         if isinstance(R, sage.rings.abc.SymbolicRing):
             raise TypeError("symbolic ring cannot be the base ring")
-        if not is_AffineSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
+        if not isinstance(domain, AffineSpace_generic) and not isinstance(domain, AlgebraicScheme_subscheme_affine):
             raise ValueError('"domain" must be an affine scheme')
 
         if R not in Fields():
@@ -523,8 +523,8 @@ def dynatomic_polynomial(self, period):
             sage: G.dehomogenize(1).dynatomic_polynomial(2)
             (1/4*c + 1/4)*x^2 + (-c - 1/2)*x + c + 1
         """
-        from sage.schemes.affine.affine_space import is_AffineSpace
-        if not is_AffineSpace(self.domain()):
+        from sage.schemes.affine.affine_space import AffineSpace_generic
+        if not isinstance(self.domain(), AffineSpace_generic):
             raise NotImplementedError("not implemented for subschemes")
         if self.domain().dimension_relative() > 1:
             raise TypeError("does not make sense in dimension >1")
@@ -1065,8 +1065,8 @@ def cyclegraph(self):
         """
         V = []
         E = []
-        from sage.schemes.affine.affine_space import is_AffineSpace
-        if is_AffineSpace(self.domain()):
+        from sage.schemes.affine.affine_space import AffineSpace_generic
+        if isinstance(self.domain(), AffineSpace_generic):
             for P in self.domain():
                 V.append(str(P))
                 Q = self(P)
diff --git a/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py b/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
index 5559a48ecce..be1ef46b251 100644
--- a/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py
@@ -34,11 +34,11 @@
 from sage.rings.infinity import Infinity
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.schemes.affine.affine_space import is_AffineSpace
+from sage.schemes.affine.affine_space import AffineSpace_generic
 from sage.schemes.berkovich.berkovich_space import (Berkovich_Cp_Affine,
-                                Berkovich_Cp_Projective, is_Berkovich_Cp,
+                                Berkovich_Cp_Projective, Berkovich_Cp,
                                 Berkovich_Element_Cp_Affine)
-from sage.schemes.projective.projective_space import is_ProjectiveSpace
+from sage.schemes.projective.projective_space import ProjectiveSpace_ring
 from sage.structure.element import Element
 
 lazy_import('sage.rings.padics.padic_base_generic', 'pAdicBaseGeneric')
@@ -241,7 +241,7 @@ def __classcall_private__(cls, dynamical_system, domain=None, ideal=None):
                     2*3^7 + 2*3^8 + 2*3^9 + 2*3^10 + 2*3^11 + 2*3^12 + 2*3^13 + 2*3^14 +
                     2*3^15 + 2*3^16 + 2*3^17 + 2*3^18 + 2*3^19 + 2*3^20 + O(3^21))
         """
-        if not (is_Berkovich_Cp(domain) or domain is None):
+        if not (isinstance(domain, Berkovich_Cp) or domain is None):
             raise TypeError('domain must be a Berkovich space over Cp, not %s' % domain)
 
         if isinstance(domain, Berkovich_Cp_Affine):
@@ -269,7 +269,7 @@ def __classcall_private__(cls, dynamical_system, domain=None, ideal=None):
         if not isinstance(morphism_domain.base_ring(), pAdicBaseGeneric):
             if morphism_domain.base_ring() in NumberFields():
                 if domain is None and ideal is not None:
-                    if is_AffineSpace(morphism_domain):
+                    if isinstance(morphism_domain, AffineSpace_generic):
                         domain = Berkovich_Cp_Affine(morphism_domain.base_ring(), ideal)
                     else:
                         domain = Berkovich_Cp_Projective(morphism_domain, ideal)
@@ -281,7 +281,7 @@ def __classcall_private__(cls, dynamical_system, domain=None, ideal=None):
                 raise ValueError('base ring of domain of dynamical_system must be p-adic or a number field '
                     'not %s' % morphism_domain.base_ring())
 
-        if is_AffineSpace(morphism_domain):
+        if isinstance(morphism_domain, AffineSpace_generic):
             return DynamicalSystem_Berkovich_affine(dynamical_system, domain)
 
         return DynamicalSystem_Berkovich_projective(dynamical_system, domain)
@@ -531,7 +531,7 @@ def __classcall_private__(cls, dynamical_system, domain=None):
                 raise TypeError('affine dynamical system passed to projective constructor')
         R = dynamical_system.base_ring()
         morphism_domain = dynamical_system.domain()
-        if not is_ProjectiveSpace(morphism_domain):
+        if not isinstance(morphism_domain, ProjectiveSpace_ring):
             raise TypeError('the domain of dynamical_system must be projective space, not %s' % morphism_domain)
         if morphism_domain.dimension_relative() != 1:
             raise ValueError('domain was not relative dimension 1')
@@ -1015,7 +1015,7 @@ def __classcall_private__(cls, dynamical_system, domain=None):
                 raise TypeError('projective dynamical system passed to affine constructor')
         R = dynamical_system.base_ring()
         morphism_domain = dynamical_system.domain()
-        if not is_AffineSpace(morphism_domain):
+        if not isinstance(morphism_domain, AffineSpace_generic):
             raise TypeError('the domain of dynamical_system must be affine space, not %s' % morphism_domain)
         if morphism_domain.dimension_relative() != 1:
             raise ValueError('domain not relative dimension 1')
diff --git a/src/sage/dynamics/arithmetic_dynamics/generic_ds.py b/src/sage/dynamics/arithmetic_dynamics/generic_ds.py
index 0afff17895c..be678cca40a 100644
--- a/src/sage/dynamics/arithmetic_dynamics/generic_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/generic_ds.py
@@ -34,9 +34,9 @@ class initialization directly.
 from sage.misc.lazy_import import lazy_import
 from sage.rings.finite_rings.finite_field_base import FiniteField
 from sage.rings.rational_field import QQ
-from sage.schemes.affine.affine_space import is_AffineSpace
+from sage.schemes.affine.affine_space import AffineSpace_generic
 from sage.schemes.affine.affine_subscheme import AlgebraicScheme_subscheme_affine
-from sage.schemes.berkovich.berkovich_space import is_Berkovich_Cp
+from sage.schemes.berkovich.berkovich_space import Berkovich_Cp
 from sage.schemes.generic.morphism import SchemeMorphism_polynomial
 
 lazy_import('sage.rings.algebraic_closure_finite_field', 'AlgebraicClosureFiniteField_generic')
@@ -165,10 +165,10 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
         if isinstance(morphism_or_polys, SchemeMorphism_polynomial):
             domain = morphism_or_polys.domain()
         if domain is not None:
-            if is_AffineSpace(domain) or isinstance(domain, AlgebraicScheme_subscheme_affine):
+            if isinstance(domain, AffineSpace_generic) or isinstance(domain, AlgebraicScheme_subscheme_affine):
                 from sage.dynamics.arithmetic_dynamics.affine_ds import DynamicalSystem_affine
                 return DynamicalSystem_affine(morphism_or_polys, domain)
-            if is_Berkovich_Cp(domain):
+            if isinstance(domain, Berkovich_Cp):
                 from sage.dynamics.arithmetic_dynamics.berkovich_ds import DynamicalSystem_Berkovich
                 return DynamicalSystem_Berkovich(morphism_or_polys,domain)
 
diff --git a/src/sage/dynamics/arithmetic_dynamics/product_projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/product_projective_ds.py
index 44565197717..706bb28cbef 100644
--- a/src/sage/dynamics/arithmetic_dynamics/product_projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/product_projective_ds.py
@@ -327,8 +327,8 @@ def cyclegraph(self):
         """
         V = []
         E = []
-        from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
-        if is_ProductProjectiveSpaces(self.domain()):
+        from sage.schemes.product_projective.space import ProductProjectiveSpaces_ring
+        if isinstance(self.domain(), ProductProjectiveSpaces_ring):
             for P in self.domain():
                 V.append(str(P))
                 Q = self(P)
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
index 4b42ad87b1f..66fdf03ecd7 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
@@ -103,12 +103,12 @@ class initialization directly.
 from sage.rings.rational_field import QQ
 from sage.rings.real_mpfr import RealField
 from sage.schemes.generic.morphism import SchemeMorphism_polynomial
-from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
+from sage.schemes.product_projective.space import ProductProjectiveSpaces_ring
 from sage.schemes.projective.projective_morphism import (
     SchemeMorphism_polynomial_projective_space,
     SchemeMorphism_polynomial_projective_space_field,
     SchemeMorphism_polynomial_projective_space_finite_field)
-from sage.schemes.projective.projective_space import ProjectiveSpace, is_ProjectiveSpace
+from sage.schemes.projective.projective_space import ProjectiveSpace, ProjectiveSpace_ring
 from sage.schemes.projective.projective_subscheme import AlgebraicScheme_subscheme_projective
 from sage.structure.element import get_coercion_model
 
@@ -374,7 +374,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
             polys = list(morphism_or_polys)
             if domain != morphism_or_polys.codomain():
                 raise ValueError('domain and codomain do not agree')
-            if not is_ProjectiveSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_projective):
+            if not isinstance(domain, ProjectiveSpace_ring) and not isinstance(domain, AlgebraicScheme_subscheme_projective):
                 raise ValueError('"domain" must be a projective scheme')
             if R not in Fields():
                 return typecall(cls, polys, domain)
@@ -430,7 +430,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
         if isinstance(R, sage.rings.abc.SymbolicRing):
             raise TypeError("the base ring cannot be the Symbolic Ring or a symbolic subring")
 
-        if is_ProductProjectiveSpaces(domain):
+        if isinstance(domain, ProductProjectiveSpaces_ring):
             splitpolys = domain._factors(polys)
             for split_poly in splitpolys:
                 split_d = domain._degree(split_poly[0])
@@ -451,7 +451,7 @@ def __classcall_private__(cls, morphism_or_polys, domain=None, names=None):
             msg = 'polys (={}) must be of the same degree'
             raise ValueError(msg.format(polys))
 
-        if not is_ProjectiveSpace(domain) and not isinstance(domain, AlgebraicScheme_subscheme_projective):
+        if not isinstance(domain, ProjectiveSpace_ring) and not isinstance(domain, AlgebraicScheme_subscheme_projective):
             raise ValueError('"domain" must be a projective scheme')
         if R not in Fields():
             return typecall(cls, polys, domain)
@@ -1264,7 +1264,7 @@ def arakelov_zhang_pairing(self, g, **kwds):
         if n <= 0:
             raise ValueError("Period must be a positive integer.")
 
-        if not (is_ProjectiveSpace(f_domain) and is_ProjectiveSpace(g_domain)):
+        if not (isinstance(f_domain, ProjectiveSpace_ring) and isinstance(g_domain, ProjectiveSpace_ring)):
             raise NotImplementedError("Not implemented for subschemes.")
 
         if f_domain.dimension_relative() > 1:
@@ -1804,7 +1804,7 @@ def primes_of_bad_reduction(self, check=True):
             sage: f.primes_of_bad_reduction()                                           # needs sage.rings.function_field
             [5, 37, 2239, 304432717]
         """
-        if (not is_ProjectiveSpace(self.domain())) or (not is_ProjectiveSpace(self.codomain())):
+        if (not isinstance(self.domain(), ProjectiveSpace_ring)) or (not isinstance(self.codomain(), ProjectiveSpace_ring)):
             raise NotImplementedError("not implemented for subschemes")
         K = FractionField(self.codomain().base_ring())
         #The primes of bad reduction are the support of the resultant for number fields
@@ -3771,7 +3771,7 @@ def critical_subscheme(self):
             TypeError: the function is not a morphism
         """
         PS = self.domain()
-        if not is_ProjectiveSpace(PS):
+        if not isinstance(PS, ProjectiveSpace_ring):
             raise NotImplementedError("not implemented for subschemes")
         if not self.is_morphism():
             raise TypeError("the function is not a morphism")
@@ -4080,7 +4080,7 @@ def is_dynamical_belyi_map(self):
             False
         """
         P = self.codomain()
-        if not is_ProjectiveSpace(P):
+        if not isinstance(P, ProjectiveSpace_ring):
             raise NotImplementedError('only implemented for dynamical systems on projective space')
         if P.dimension_relative() != 1:
             raise NotImplementedError('only implemented for maps on projective space of dimension 1')
@@ -5238,7 +5238,7 @@ def multiplier_spectra(self, n, formal=False, type='point', use_algebraic_closur
 
         if (n < 1):
             raise ValueError("period must be a positive integer")
-        if not is_ProjectiveSpace(PS):
+        if not isinstance(PS, ProjectiveSpace_ring):
             raise NotImplementedError("not implemented for subschemes")
 
         if PS.dimension_relative() > 1:
@@ -5746,7 +5746,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point',
         if n < 1:
             raise ValueError("period must be a positive integer")
         dom = self.domain()
-        if not is_ProjectiveSpace(dom):
+        if not isinstance(dom, ProjectiveSpace_ring):
             raise NotImplementedError("not implemented for subschemes")
         if self.degree() <= 1:
             raise TypeError("must have degree at least 2")
@@ -6397,7 +6397,7 @@ def _is_preperiodic(self, P, err=0.1, return_period=False):
             True
         """
         codomain = self.codomain()
-        if not is_ProjectiveSpace(codomain):
+        if not isinstance(codomain, ProjectiveSpace_ring):
             # in order to calculate the canonical height, we need
             # this map to be a morphism of projective space
             ambient_space = codomain.ambient_space()
@@ -6516,7 +6516,7 @@ def postcritical_set(self, check=True):
             sage: g.postcritical_set()
             [(1 : 0), (0 : 1), (a + 2 : 1)]
         """
-        if not is_ProjectiveSpace(self.domain()):
+        if not isinstance(self.domain(), ProjectiveSpace_ring):
             raise ValueError('must be a dynamical system on projective space')
         if self.domain().dimension_relative() != 1:
             raise ValueError('must be defined on projective space of dimension 1')
@@ -9106,7 +9106,7 @@ def cyclegraph(self):
         """
         V = []
         E = []
-        if is_ProjectiveSpace(self.domain()):
+        if isinstance(self.domain(), ProjectiveSpace_ring):
             for P in self.domain():
                 V.append(P)
                 try:
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx b/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
index f05806f4935..08efef94554 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
@@ -82,8 +82,8 @@ cpdef _fast_possible_periods(self, return_points=False):
         raise TypeError("must be prime field")
 
     PS = self.domain()
-    from sage.schemes.projective.projective_space import is_ProjectiveSpace
-    if not is_ProjectiveSpace(PS) or PS != self.codomain():
+    from sage.schemes.projective.projective_space import ProjectiveSpace_ring
+    if not isinstance(PS, ProjectiveSpace_ring) or PS != self.codomain():
         raise NotImplementedError("must be an endomorphism of projective space")
 
     p = PS.base_ring().order()
diff --git a/src/sage/schemes/affine/affine_homset.py b/src/sage/schemes/affine/affine_homset.py
index b6570bd6f6d..a54d4d68c3c 100644
--- a/src/sage/schemes/affine/affine_homset.py
+++ b/src/sage/schemes/affine/affine_homset.py
@@ -261,10 +261,10 @@ def points(self, **kwds):
             may be computed partially or incorrectly.
             [(0.0, 0.0)]
         """
-        from sage.schemes.affine.affine_space import is_AffineSpace
+        from sage.schemes.affine.affine_space import AffineSpace_generic
 
         X = self.codomain()
-        if not is_AffineSpace(X) and X.base_ring() in Fields():
+        if not isinstance(X, AffineSpace_generic) and X.base_ring() in Fields():
             if hasattr(X.base_ring(), 'precision'):
                 numerical = True
                 verbose("Warning: computations in the numerical fields are inexact;points may be computed partially or incorrectly.", level=0)
@@ -436,7 +436,7 @@ def numerical_points(self, F=None, **kwds):
             ...
             ValueError: tolerance must be positive
         """
-        from sage.schemes.affine.affine_space import is_AffineSpace
+        from sage.schemes.affine.affine_space import AffineSpace_generic
         if F is None:
             F = CC
         if F not in Fields() or not hasattr(F, 'precision'):
@@ -446,7 +446,7 @@ def numerical_points(self, F=None, **kwds):
             raise TypeError('base ring must be a number field')
 
         AA = X.ambient_space().change_ring(F)
-        if not is_AffineSpace(X) and X.base_ring() in Fields():
+        if not isinstance(X, AffineSpace_generic) and X.base_ring() in Fields():
             # Then X must be a subscheme
             dim_ideal = X.defining_ideal().dimension()
             if dim_ideal != 0:  # no points
diff --git a/src/sage/schemes/affine/affine_point.py b/src/sage/schemes/affine/affine_point.py
index 00779dbb2d6..4e09c1e133a 100644
--- a/src/sage/schemes/affine/affine_point.py
+++ b/src/sage/schemes/affine/affine_point.py
@@ -372,8 +372,8 @@ def intersection_multiplicity(self, X):
             ...
             TypeError: this point must be a point on an affine subscheme
         """
-        from sage.schemes.affine.affine_space import is_AffineSpace
-        if is_AffineSpace(self.codomain()):
+        from sage.schemes.affine.affine_space import AffineSpace_generic
+        if isinstance(self.codomain(), AffineSpace_generic):
             raise TypeError("this point must be a point on an affine subscheme")
         return self.codomain().intersection_multiplicity(X, self)
 
@@ -397,8 +397,8 @@ def multiplicity(self):
             sage: Q2.multiplicity()                                                     # needs sage.libs.singular
             2
         """
-        from sage.schemes.affine.affine_space import is_AffineSpace
-        if is_AffineSpace(self.codomain()):
+        from sage.schemes.affine.affine_space import AffineSpace_generic
+        if isinstance(self.codomain(), AffineSpace_generic):
             raise TypeError("this point must be a point on an affine subscheme")
         return self.codomain().multiplicity(self)
 
diff --git a/src/sage/schemes/affine/affine_rational_point.py b/src/sage/schemes/affine/affine_rational_point.py
index 4ac17a60d79..ff0b88c31f9 100644
--- a/src/sage/schemes/affine/affine_rational_point.py
+++ b/src/sage/schemes/affine/affine_rational_point.py
@@ -54,7 +54,7 @@
 
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.schemes.generic.scheme import is_Scheme
+from sage.schemes.generic.scheme import Scheme
 
 
 def enum_affine_rational_field(X, B):
@@ -108,12 +108,12 @@ def enum_affine_rational_field(X, B):
 
     - Raman Raghukul 2018: updated.
     """
-    from sage.schemes.affine.affine_space import is_AffineSpace
-    if is_Scheme(X):
-        if not is_AffineSpace(X.ambient_space()):
+    from sage.schemes.affine.affine_space import AffineSpace_generic
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), AffineSpace_generic):
             raise TypeError("ambient space must be affine space over the rational field")
         X = X(X.base_ring())
-    elif not is_AffineSpace(X.codomain().ambient_space()):
+    elif not isinstance(X.codomain().ambient_space(), AffineSpace_generic):
         raise TypeError("codomain must be affine space over the rational field")
 
     n = X.codomain().ambient_space().ngens()
@@ -215,12 +215,12 @@ def enum_affine_number_field(X, **kwds):
     B = kwds.pop('bound')
     tol = kwds.pop('tolerance', 1e-2)
     prec = kwds.pop('precision', 53)
-    from sage.schemes.affine.affine_space import is_AffineSpace
-    if is_Scheme(X):
-        if not is_AffineSpace(X.ambient_space()):
+    from sage.schemes.affine.affine_space import AffineSpace_generic
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), AffineSpace_generic):
             raise TypeError("ambient space must be affine space over a number field")
         X = X(X.base_ring())
-    elif not is_AffineSpace(X.codomain().ambient_space()):
+    elif not isinstance(X.codomain().ambient_space(), AffineSpace_generic):
         raise TypeError("codomain must be affine space over a number field")
 
     R = X.codomain().ambient_space()
@@ -289,12 +289,12 @@ def enum_affine_finite_field(X):
 
     - John Cremona and Charlie Turner (06-2010)
     """
-    from sage.schemes.affine.affine_space import is_AffineSpace
-    if is_Scheme(X):
-        if not is_AffineSpace(X.ambient_space()):
+    from sage.schemes.affine.affine_space import AffineSpace_generic
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), AffineSpace_generic):
             raise TypeError("ambient space must be affine space over a finite field")
         X = X(X.base_ring())
-    elif not is_AffineSpace(X.codomain().ambient_space()):
+    elif not isinstance(X.codomain().ambient_space(), AffineSpace_generic):
         raise TypeError("codomain must be affine space over a finite field")
 
     n = X.codomain().ambient_space().ngens()
diff --git a/src/sage/schemes/affine/affine_space.py b/src/sage/schemes/affine/affine_space.py
index 05d3c5b59e3..76316311615 100644
--- a/src/sage/schemes/affine/affine_space.py
+++ b/src/sage/schemes/affine/affine_space.py
@@ -46,12 +46,17 @@ def is_AffineSpace(x) -> bool:
 
         sage: from sage.schemes.affine.affine_space import is_AffineSpace
         sage: is_AffineSpace(AffineSpace(5, names='x'))
+        doctest:warning...
+        DeprecationWarning: The function is_AffineSpace is deprecated; use 'isinstance(..., AffineSpace_generic)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
         sage: is_AffineSpace(AffineSpace(5, GF(9, 'alpha'), names='x'))                 # needs sage.rings.finite_rings
         True
         sage: is_AffineSpace(Spec(ZZ))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_AffineSpace is deprecated; use 'isinstance(..., AffineSpace_generic)' instead.")
     return isinstance(x, AffineSpace_generic)
 
 
diff --git a/src/sage/schemes/berkovich/berkovich_space.py b/src/sage/schemes/berkovich/berkovich_space.py
index 100c2807b9d..766ae7c4388 100644
--- a/src/sage/schemes/berkovich/berkovich_space.py
+++ b/src/sage/schemes/berkovich/berkovich_space.py
@@ -35,8 +35,8 @@
 from sage.schemes.berkovich.berkovich_cp_element import (Berkovich_Element_Cp_Affine,
                                                          Berkovich_Element_Cp_Projective)
 from sage.structure.parent import Parent
-from sage.schemes.affine.affine_space import is_AffineSpace
-from sage.schemes.projective.projective_space import is_ProjectiveSpace, ProjectiveSpace
+from sage.schemes.affine.affine_space import AffineSpace_generic
+from sage.schemes.projective.projective_space import ProjectiveSpace_ring, ProjectiveSpace
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.categories.number_fields import NumberFields
 import sage.rings.abc
@@ -60,8 +60,13 @@ def is_Berkovich(space) -> bool:
         sage: B = Berkovich_Cp_Projective(3)
         sage: from sage.schemes.berkovich.berkovich_space import is_Berkovich
         sage: is_Berkovich(B)
+        doctest:warning...
+        DeprecationWarning: The function is_Berkovich is deprecated; use 'isinstance(..., Berkovich)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_Berkovich is deprecated; use 'isinstance(..., Berkovich)' instead.")
     return isinstance(space, Berkovich)
 
 
@@ -77,10 +82,15 @@ def is_Berkovich_Cp(space) -> bool:
     EXAMPLES::
 
         sage: B = Berkovich_Cp_Projective(3)
-        sage: from sage.schemes.berkovich.berkovich_space import is_Berkovich
-        sage: is_Berkovich(B)
+        sage: from sage.schemes.berkovich.berkovich_space import is_Berkovich_Cp
+        sage: is_Berkovich_Cp(B)
+        doctest:warning...
+        DeprecationWarning: The function is_Berkovich_Cp is deprecated; use 'isinstance(..., Berkovich_Cp)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_Berkovich_Cp is deprecated; use 'isinstance(..., Berkovich_Cp)' instead.")
     return isinstance(space, Berkovich_Cp)
 
 
@@ -433,7 +443,7 @@ def __init__(self, base, ideal=None):
                 base = Qp(base)  # change to Qpbar
             else:
                 raise ValueError("non-prime passed into Berkovich space")
-        if is_AffineSpace(base):
+        if isinstance(base, AffineSpace_generic):
             base = base.base_ring()
         if base in NumberFields():
             if ideal is None:
@@ -630,7 +640,7 @@ def __init__(self, base, ideal=None):
                 raise ValueError("non-prime passed into Berkovich space")
         if base in NumberFields() or isinstance(base, sage.rings.abc.pAdicField):
             base = ProjectiveSpace(base, 1)
-        if not is_ProjectiveSpace(base):
+        if not isinstance(base, ProjectiveSpace_ring):
             try:
                 base = ProjectiveSpace(base)
             except (TypeError, ValueError):
diff --git a/src/sage/schemes/curves/affine_curve.py b/src/sage/schemes/curves/affine_curve.py
index efbc690b543..b3ed871794f 100644
--- a/src/sage/schemes/curves/affine_curve.py
+++ b/src/sage/schemes/curves/affine_curve.py
@@ -149,7 +149,7 @@
 from sage.rings.rational_field import is_RationalField
 from sage.rings.infinity import infinity
 
-from sage.schemes.affine.affine_space import AffineSpace, is_AffineSpace
+from sage.schemes.affine.affine_space import AffineSpace, AffineSpace_generic
 from sage.schemes.affine.affine_subscheme import (AlgebraicScheme_subscheme_affine,
                                                   AlgebraicScheme_subscheme_affine_field)
 
@@ -209,7 +209,7 @@ def __init__(self, A, X):
             sage: C = Curve([x^2 - z, z - 8*x], A); C
             Affine Curve over Finite Field of size 7 defined by x^2 - z, -x + z
         """
-        if not is_AffineSpace(A):
+        if not isinstance(A, AffineSpace_generic):
             raise TypeError("A (={}) must be an affine space".format(A))
 
         Curve_generic.__init__(self, A, X)
@@ -299,7 +299,7 @@ def __init__(self, A, f):
             Affine Plane Curve over Complex Field with 53 bits of precision defined
             by x^2 + y^2
         """
-        if not (is_AffineSpace(A) and A.dimension != 2):
+        if not (isinstance(A, AffineSpace_generic) and A.dimension != 2):
             raise TypeError("Argument A (= %s) must be an affine plane." % A)
 
         super().__init__(A, [f])
@@ -464,7 +464,7 @@ def plot(self, *args, **kwds):
         A 5-nodal curve of degree 11.  This example also illustrates
         some of the optional arguments::
 
-            sage: # needs sage.plot()
+            sage: # needs sage.plot
             sage: R.<x, y> = ZZ[]
             sage: C = Curve(32*x^2 - 2097152*y^11 + 1441792*y^9
             ....:            - 360448*y^7 + 39424*y^5 - 1760*y^3 + 22*y - 1)
@@ -998,7 +998,7 @@ def projection(self, indices, AS=None):
         if len(set(indices)) < len(indices):
             raise ValueError("(=%s) must be a list or tuple of distinct indices or variables" % indices)
         if AS is not None:
-            if not is_AffineSpace(AS):
+            if not isinstance(AS, AffineSpace_generic):
                 raise TypeError("(=%s) must be an affine space" % AS)
             if AS.dimension_relative() != len(indices):
                 raise TypeError("(=%s) must have dimension (=%s)" % (AS, len(indices)))
diff --git a/src/sage/schemes/curves/constructor.py b/src/sage/schemes/curves/constructor.py
index 3564cfd73cc..a49b2002495 100644
--- a/src/sage/schemes/curves/constructor.py
+++ b/src/sage/schemes/curves/constructor.py
@@ -46,10 +46,10 @@
 
 from sage.structure.all import Sequence
 
-from sage.schemes.generic.ambient_space import is_AmbientSpace
-from sage.schemes.generic.algebraic_scheme import is_AlgebraicScheme
-from sage.schemes.affine.affine_space import AffineSpace, is_AffineSpace
-from sage.schemes.projective.projective_space import ProjectiveSpace, is_ProjectiveSpace
+from sage.schemes.generic.ambient_space import AmbientSpace
+from sage.schemes.generic.algebraic_scheme import AlgebraicScheme
+from sage.schemes.affine.affine_space import AffineSpace, AffineSpace_generic
+from sage.schemes.projective.projective_space import ProjectiveSpace, ProjectiveSpace_ring
 from sage.schemes.plane_conics.constructor import Conic
 
 from .projective_curve import (ProjectiveCurve,
@@ -233,10 +233,10 @@ def Curve(F, A=None):
         0
     """
     if A is None:
-        if is_AmbientSpace(F) and F.dimension() == 1:
+        if isinstance(F, AmbientSpace) and F.dimension() == 1:
             return Curve(F.coordinate_ring().zero(), F)
 
-        if is_AlgebraicScheme(F):
+        if isinstance(F, AlgebraicScheme):
             return Curve(F.defining_polynomials(), F.ambient_space())
 
         if isinstance(F, (list, tuple)):
@@ -291,7 +291,7 @@ def Curve(F, A=None):
         else:
             raise TypeError("F (={}) must be a multivariate polynomial".format(F))
     else:
-        if not is_AmbientSpace(A):
+        if not isinstance(A, AmbientSpace):
             raise TypeError("ambient space must be either an affine or projective space")
         if not isinstance(F, (list, tuple)):
             F = [F]
@@ -304,7 +304,7 @@ def Curve(F, A=None):
 
     k = A.base_ring()
 
-    if is_AffineSpace(A):
+    if isinstance(A, AffineSpace_generic):
         if n == 1:
             if A.coordinate_ring().ideal(F).is_zero():
                 if isinstance(k, FiniteField):
@@ -337,7 +337,7 @@ def Curve(F, A=None):
             return AffinePlaneCurve_field(A, F)
         return AffinePlaneCurve(A, F)
 
-    elif is_ProjectiveSpace(A):
+    elif isinstance(A, ProjectiveSpace_ring):
         if n == 1:
             if A.coordinate_ring().ideal(F).is_zero():
                 if isinstance(k, FiniteField):
diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
index 1cc7fce0906..fb1edc7d0ad 100644
--- a/src/sage/schemes/curves/projective_curve.py
+++ b/src/sage/schemes/curves/projective_curve.py
@@ -158,7 +158,7 @@
 from sage.rings.rational_field import is_RationalField
 from sage.rings.integer import Integer
 
-from sage.schemes.projective.projective_space import ProjectiveSpace, is_ProjectiveSpace
+from sage.schemes.projective.projective_space import ProjectiveSpace, ProjectiveSpace_ring
 
 from sage.schemes.projective.projective_subscheme import (AlgebraicScheme_subscheme_projective,
                                                           AlgebraicScheme_subscheme_projective_field)
@@ -215,7 +215,7 @@ def __init__(self, A, X, category=None):
             sage: loads(dumps(C)) == C
             True
         """
-        if not is_ProjectiveSpace(A):
+        if not isinstance(A, ProjectiveSpace_ring):
             raise TypeError("A (=%s) must be a projective space" % A)
 
         Curve_generic.__init__(self, A, X, category=category)
@@ -419,7 +419,7 @@ def projection(self, P=None, PS=None):
         if self.base_ring() not in Fields():
             raise TypeError("this curve must be defined over a field")
         if PS is not None:
-            if not is_ProjectiveSpace(PS):
+            if not isinstance(PS, ProjectiveSpace_ring):
                 raise TypeError("(=%s) must be a projective space" % PS)
             if PS.dimension_relative() != n - 1:
                 raise TypeError("(=%s) must have dimension (=%s)" % (PS, n - 1))
@@ -621,7 +621,7 @@ def __init__(self, A, f, category=None):
             sage: loads(dumps(C)) == C
             True
         """
-        if not (is_ProjectiveSpace(A) and A.dimension != 2):
+        if not (isinstance(A, ProjectiveSpace_ring) and A.dimension != 2):
             raise TypeError("the ambient space is not a projective plane")
 
         super().__init__(A, [f], category=category)
diff --git a/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py b/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
index 3dc8ea0f11e..c3cdd991e58 100644
--- a/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
+++ b/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
@@ -94,7 +94,7 @@
 from sage.rings.fraction_field import FractionField
 
 from sage.schemes.elliptic_curves.constructor import EllipticCurve
-from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
+from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
 
 from sage.schemes.elliptic_curves.weierstrass_morphism \
         import WeierstrassIsomorphism, _isomorphisms, baseWI, negation_morphism
@@ -1042,7 +1042,7 @@ def __init__(self, E, kernel, codomain=None, degree=None, model=None, check=True
                to Elliptic Curve defined by y^2 + x*y = x^3 - x^2 - 5252*x - 178837
                   over Rational Field
         """
-        if not is_EllipticCurve(E):
+        if not isinstance(E, EllipticCurve_generic):
             raise ValueError("given E is not an elliptic curve")
 
         if not isinstance(kernel, list) and kernel in E:
@@ -1854,7 +1854,7 @@ def __setup_post_isomorphism(self, codomain, model):
             codomain = compute_model(oldE2, model)
 
         else:  # codomain is not None
-            if not is_EllipticCurve(codomain):
+            if not isinstance(codomain, EllipticCurve_generic):
                 raise ValueError("given codomain is not an elliptic curve")
 
             if not oldE2.is_isomorphic(codomain):
diff --git a/src/sage/schemes/elliptic_curves/ell_field.py b/src/sage/schemes/elliptic_curves/ell_field.py
index 3efa79ff759..237c838b3d4 100644
--- a/src/sage/schemes/elliptic_curves/ell_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_field.py
@@ -444,10 +444,10 @@ def is_quadratic_twist(self, other):
             sage: E1.is_isomorphic(E2)
             True
         """
-        from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
+        from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
         E = self
         F = other
-        if not is_EllipticCurve(E) or not is_EllipticCurve(F):
+        if not isinstance(E, EllipticCurve_generic) or not isinstance(F, EllipticCurve_generic):
             raise ValueError("arguments are not elliptic curves")
         K = E.base_ring()
         zero = K.zero()
@@ -543,10 +543,10 @@ def is_quartic_twist(self, other):
             sage: (D/12345).is_perfect_power(4)
             True
         """
-        from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
+        from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
         E = self
         F = other
-        if not is_EllipticCurve(E) or not is_EllipticCurve(F):
+        if not isinstance(E, EllipticCurve_generic) or not isinstance(F, EllipticCurve_generic):
             raise ValueError("arguments are not elliptic curves")
         K = E.base_ring()
         zero = K.zero()
@@ -612,10 +612,10 @@ def is_sextic_twist(self, other):
             sage: (D/12345).is_perfect_power(6)
             True
         """
-        from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
+        from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
         E = self
         F = other
-        if not is_EllipticCurve(E) or not is_EllipticCurve(F):
+        if not isinstance(E, EllipticCurve_generic) or not isinstance(F, EllipticCurve_generic):
             raise ValueError("arguments are not elliptic curves")
         K = E.base_ring()
         zero = K.zero()
@@ -2065,8 +2065,8 @@ def is_isogenous(self, other, field=None):
             ...
             NotImplementedError: Only implemented for isomorphic curves over general fields.
         """
-        from .ell_generic import is_EllipticCurve
-        if not is_EllipticCurve(other):
+        from .ell_generic import EllipticCurve_generic
+        if not isinstance(other, EllipticCurve_generic):
             raise ValueError("Second argument is not an Elliptic Curve.")
         if self.is_isomorphic(other):
             return True
diff --git a/src/sage/schemes/elliptic_curves/ell_finite_field.py b/src/sage/schemes/elliptic_curves/ell_finite_field.py
index f67e15b5627..5ffd2dc6c0e 100644
--- a/src/sage/schemes/elliptic_curves/ell_finite_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_finite_field.py
@@ -1252,8 +1252,8 @@ def is_isogenous(self, other, field=None, proof=True):
             sage: E1.is_isogenous(E7,GF(13^30,'j'))
             False
         """
-        from .ell_generic import is_EllipticCurve
-        if not is_EllipticCurve(other):
+        from .ell_generic import EllipticCurve_generic
+        if not isinstance(other, EllipticCurve_generic):
             raise ValueError("Second argument is not an Elliptic Curve.")
         if self.is_isomorphic(other):
             return True
diff --git a/src/sage/schemes/elliptic_curves/ell_generic.py b/src/sage/schemes/elliptic_curves/ell_generic.py
index 4719b914bde..2e950ae3bc9 100644
--- a/src/sage/schemes/elliptic_curves/ell_generic.py
+++ b/src/sage/schemes/elliptic_curves/ell_generic.py
@@ -98,10 +98,15 @@ def is_EllipticCurve(x):
         sage: from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
         sage: E = EllipticCurve([1,2,3/4,7,19])
         sage: is_EllipticCurve(E)
+        doctest:warning...
+        DeprecationWarning: The function is_EllipticCurve is deprecated; use 'isinstance(..., EllipticCurve_generic)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
         sage: is_EllipticCurve(0)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_EllipticCurve is deprecated; use 'isinstance(..., EllipticCurve_generic)' instead.")
     return isinstance(x, EllipticCurve_generic)
 
 
@@ -2908,7 +2913,7 @@ def is_isomorphic(self, other, field=None):
             sage: E.is_isomorphic(F.change_ring(CC))
             False
         """
-        if not is_EllipticCurve(other):
+        if not isinstance(other, EllipticCurve_generic):
             return False
         if field is None:
             if self.base_ring() != other.base_ring():
diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py
index b0c07df78b6..298cf9277d7 100644
--- a/src/sage/schemes/elliptic_curves/ell_number_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py
@@ -92,7 +92,7 @@
 
 import sage.rings.abc
 from .ell_field import EllipticCurve_field
-from .ell_generic import is_EllipticCurve
+from .ell_generic import EllipticCurve_generic
 from .ell_point import EllipticCurvePoint_number_field
 from .constructor import EllipticCurve
 from sage.rings.integer_ring import ZZ
@@ -3176,7 +3176,7 @@ def is_isogenous(self, other, proof=True, maxnorm=100):
             sage: EK.is_isogenous(EcK)      # long time (about 3.5 s)
             True
         """
-        if not is_EllipticCurve(other):
+        if not isinstance(other, EllipticCurve_generic):
             raise ValueError("Second argument is not an Elliptic Curve.")
         if self.is_isomorphic(other):
             return True
diff --git a/src/sage/schemes/elliptic_curves/ell_rational_field.py b/src/sage/schemes/elliptic_curves/ell_rational_field.py
index ce77cdca614..44e26cb6f1f 100644
--- a/src/sage/schemes/elliptic_curves/ell_rational_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_rational_field.py
@@ -52,7 +52,7 @@
 
 from . import constructor
 from . import BSD
-from .ell_generic import is_EllipticCurve
+from .ell_generic import EllipticCurve_generic
 from . import ell_modular_symbols
 from .ell_number_field import EllipticCurve_number_field
 from . import ell_point
@@ -4985,7 +4985,7 @@ def is_isogenous(self, other, proof=True, maxp=200):
             sage: E.is_isogenous(EE)
             False
         """
-        if not is_EllipticCurve(other):
+        if not isinstance(other, EllipticCurve_generic):
             raise ValueError("Second argument is not an Elliptic Curve.")
         if other.base_field() is not QQ:
             raise ValueError("If first argument is an elliptic curve over QQ then the second argument must be also.")
diff --git a/src/sage/schemes/elliptic_curves/heegner.py b/src/sage/schemes/elliptic_curves/heegner.py
index f0ad1420bcf..868f28d025d 100644
--- a/src/sage/schemes/elliptic_curves/heegner.py
+++ b/src/sage/schemes/elliptic_curves/heegner.py
@@ -5762,8 +5762,8 @@ def kolyvagin_reduction_data(E, q, first_only=True):
         sage: kolyvagin_reduction_data(EllipticCurve('2350g1'), 5, first_only=False)
         (19, 239, -311, 19, 6480, 85680)
     """
-    from .ell_generic import is_EllipticCurve
-    if not is_EllipticCurve(E):
+    from .ell_generic import EllipticCurve_generic
+    if not isinstance(E, EllipticCurve_generic):
         raise TypeError("E must be an elliptic curve")
 
     q = ZZ(q)
diff --git a/src/sage/schemes/elliptic_curves/height.py b/src/sage/schemes/elliptic_curves/height.py
index 7ddd080d5b1..920cf47b676 100644
--- a/src/sage/schemes/elliptic_curves/height.py
+++ b/src/sage/schemes/elliptic_curves/height.py
@@ -805,8 +805,8 @@ def __init__(self, E):
             ValueError: EllipticCurveCanonicalHeight class can only be created
             from an elliptic curve defined over a number field
         """
-        from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
-        if is_EllipticCurve(E):
+        from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
+        if isinstance(E, EllipticCurve_generic):
             self.E = E
             from sage.rings.number_field.number_field_base import NumberField
             K = E.base_ring()
diff --git a/src/sage/schemes/elliptic_curves/jacobian.py b/src/sage/schemes/elliptic_curves/jacobian.py
index fcd941b4276..9099a803afc 100644
--- a/src/sage/schemes/elliptic_curves/jacobian.py
+++ b/src/sage/schemes/elliptic_curves/jacobian.py
@@ -111,8 +111,8 @@ def Jacobian(X, **kwds):
         else:
             return Jacobian_of_equation(X, **kwds)
 
-    from sage.schemes.generic.scheme import is_Scheme
-    if is_Scheme(X) and X.dimension() == 1:
+    from sage.schemes.generic.scheme import Scheme
+    if isinstance(X, Scheme) and X.dimension() == 1:
         return Jacobian_of_curve(X, morphism=morphism, **kwds)
 
 
diff --git a/src/sage/schemes/elliptic_curves/weierstrass_morphism.py b/src/sage/schemes/elliptic_curves/weierstrass_morphism.py
index 878b5a78d82..30a2e4bd538 100644
--- a/src/sage/schemes/elliptic_curves/weierstrass_morphism.py
+++ b/src/sage/schemes/elliptic_curves/weierstrass_morphism.py
@@ -295,8 +295,8 @@ def _isomorphisms(E, F):
         sage: all({iso2*iso1 for iso1 in Iso} == set(Aut) for iso2 in F.isomorphisms(E))
         True
     """
-    from .ell_generic import is_EllipticCurve
-    if not is_EllipticCurve(E) or not is_EllipticCurve(F):
+    from .ell_generic import EllipticCurve_generic
+    if not isinstance(E, EllipticCurve_generic) or not isinstance(F, EllipticCurve_generic):
         raise ValueError("arguments are not elliptic curves")
 
     j = E.j_invariant()
@@ -459,13 +459,13 @@ def __init__(self, E=None, urst=None, F=None):
             sage: type(iso.degree())                                                    # needs sage.rings.finite_rings
             <class 'sage.rings.integer.Integer'>
         """
-        from .ell_generic import is_EllipticCurve
+        from .ell_generic import EllipticCurve_generic
 
         if E is not None:
-            if not is_EllipticCurve(E):
+            if not isinstance(E, EllipticCurve_generic):
                 raise ValueError("first argument must be an elliptic curve or None")
         if F is not None:
-            if not is_EllipticCurve(F):
+            if not isinstance(F, EllipticCurve_generic):
                 raise ValueError("third argument must be an elliptic curve or None")
         if urst is not None:
             if len(urst) != 4:
diff --git a/src/sage/schemes/generic/algebraic_scheme.py b/src/sage/schemes/generic/algebraic_scheme.py
index 172256fa6a1..badd0531533 100644
--- a/src/sage/schemes/generic/algebraic_scheme.py
+++ b/src/sage/schemes/generic/algebraic_scheme.py
@@ -159,6 +159,9 @@ def is_AlgebraicScheme(x):
           x^2 + y^2
         sage: from sage.schemes.generic.algebraic_scheme import is_AlgebraicScheme
         sage: is_AlgebraicScheme(V)
+        doctest:warning...
+        DeprecationWarning: The function is_AlgebraicScheme is deprecated; use 'isinstance(..., AlgebraicScheme)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
 
     Affine space is itself not an algebraic scheme, though the closed
@@ -190,6 +193,8 @@ def is_AlgebraicScheme(x):
         sage: is_AlgebraicScheme(S)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_AlgebraicScheme is deprecated; use 'isinstance(..., AlgebraicScheme)' instead.")
     return isinstance(x, AlgebraicScheme)
 
 
@@ -227,7 +232,7 @@ def __init__(self, A, category=None):
             sage: S.category()
             Category of schemes over Integer Ring
         """
-        if not ambient_space.is_AmbientSpace(A):
+        if not isinstance(A, ambient_space.AmbientSpace):
             raise TypeError("A (=%s) must be an ambient space")
         self.__A = A
         self.__divisor_group = {}
@@ -675,7 +680,7 @@ def _latex_(self):
              X \\text{ is defined by }\\text{no polynomials},\\text{ and }
              Y \\text{ is defined by } x - y.'
         """
-        if sage.schemes.affine.affine_space.is_AffineSpace(self.ambient_space()):
+        if isinstance(self.ambient_space(), sage.schemes.affine.affine_space.AffineSpace_generic):
             t = "affine"
         else:
             t = "projective"
@@ -709,7 +714,7 @@ def _repr_(self):
             sage: U._repr_()
             'Quasi-projective subscheme X - Y of Projective Space of dimension 2 over Integer Ring, where X is defined by:\n  (no polynomials)\nand Y is defined by:\n  x - y'
         """
-        if sage.schemes.affine.affine_space.is_AffineSpace(self.ambient_space()):
+        if isinstance(self.ambient_space(), sage.schemes.affine.affine_space.AffineSpace_generic):
             t = "affine"
         else:
             t = "projective"
diff --git a/src/sage/schemes/generic/ambient_space.py b/src/sage/schemes/generic/ambient_space.py
index 52b3f1e0e39..6706e6adde8 100644
--- a/src/sage/schemes/generic/ambient_space.py
+++ b/src/sage/schemes/generic/ambient_space.py
@@ -25,6 +25,9 @@ def is_AmbientSpace(x):
 
         sage: from sage.schemes.generic.ambient_space import is_AmbientSpace
         sage: is_AmbientSpace(ProjectiveSpace(3, ZZ))
+        doctest:warning...
+        DeprecationWarning: The function is_AmbientSpace is deprecated; use 'isinstance(..., AmbientSpace)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
         sage: is_AmbientSpace(AffineSpace(2, QQ))
         True
@@ -32,8 +35,11 @@ def is_AmbientSpace(x):
         sage: is_AmbientSpace(P.subscheme([x + y + z]))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_AmbientSpace is deprecated; use 'isinstance(..., AmbientSpace)' instead.")
     return isinstance(x, AmbientSpace)
 
+
 class AmbientSpace(Scheme):
     """
     Base class for ambient spaces over a ring.
diff --git a/src/sage/schemes/generic/divisor.py b/src/sage/schemes/generic/divisor.py
index c6d99b12204..8b41d473487 100644
--- a/src/sage/schemes/generic/divisor.py
+++ b/src/sage/schemes/generic/divisor.py
@@ -48,8 +48,8 @@
 from sage.structure.formal_sum import FormalSum
 
 from .morphism import is_SchemeMorphism
-from sage.schemes.affine.affine_space import is_AffineSpace
-from sage.schemes.projective.projective_space import is_ProjectiveSpace
+from sage.schemes.affine.affine_space import AffineSpace_generic
+from sage.schemes.projective.projective_space import ProjectiveSpace_ring
 
 
 def CurvePointToIdeal(C,P):
@@ -72,7 +72,7 @@ def CurvePointToIdeal(C,P):
     m = n-1
     while m > 0 and P[m] == 0:
         m += -1
-    if is_ProjectiveSpace(A):
+    if isinstance(A, ProjectiveSpace_ring):
         a_m = P[m]
         x_m = x[m]
         for i in range(m):
@@ -81,7 +81,7 @@ def CurvePointToIdeal(C,P):
                 polys.append(x[i])
             else:
                 polys.append(a_m*x[i]-ai*x_m)
-    elif is_AffineSpace(A):
+    elif isinstance(A, AffineSpace_generic):
         for i in range(m+1):
             ai = P[i]
             if ai == 0:
diff --git a/src/sage/schemes/generic/divisor_group.py b/src/sage/schemes/generic/divisor_group.py
index 5dfd66a1bb9..a0890cd717a 100644
--- a/src/sage/schemes/generic/divisor_group.py
+++ b/src/sage/schemes/generic/divisor_group.py
@@ -75,10 +75,15 @@ def is_DivisorGroup(x):
         sage: from sage.schemes.generic.divisor_group import is_DivisorGroup, DivisorGroup
         sage: Div = DivisorGroup(Spec(ZZ), base_ring=QQ)
         sage: is_DivisorGroup(Div)
+        doctest:warning...
+        DeprecationWarning: The function is_DivisorGroup is deprecated; use 'isinstance(..., DivisorGroup_generic)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
         sage: is_DivisorGroup('not a divisor')
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_DivisorGroup is deprecated; use 'isinstance(..., DivisorGroup_generic)' instead.")
     return isinstance(x, DivisorGroup_generic)
 
 
diff --git a/src/sage/schemes/generic/homset.py b/src/sage/schemes/generic/homset.py
index 6fca9c1e257..20d1398dcb7 100644
--- a/src/sage/schemes/generic/homset.py
+++ b/src/sage/schemes/generic/homset.py
@@ -67,12 +67,17 @@ def is_SchemeHomset(H):
           Defn: Identity map
         sage: from sage.schemes.generic.homset import is_SchemeHomset
         sage: is_SchemeHomset(f)
+        doctest:warning...
+        DeprecationWarning: The function is_SchemeHomset is deprecated; use 'isinstance(..., SchemeHomset_generic)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         False
         sage: is_SchemeHomset(f.parent())
         True
         sage: is_SchemeHomset('a string')
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_SchemeHomset is deprecated; use 'isinstance(..., SchemeHomset_generic)' instead.")
     return isinstance(H, SchemeHomset_generic)
 
 
@@ -164,7 +169,7 @@ def create_key_and_extra_args(self, X, Y, category=None, base=None,
         if base is None:
             from sage.structure.element import coercion_model
             base = coercion_model.common_parent(X.base_ring(), Y.base_ring())
-        if is_AffineScheme(base):
+        if isinstance(base, AffineScheme):
             base_spec = base
             base_ring = base.coordinate_ring()
         elif base in _CommRings:
@@ -327,7 +332,7 @@ def natural_map(self):
         """
         X = self.domain()
         Y = self.codomain()
-        if is_AffineScheme(Y) and Y.coordinate_ring() == X.base_ring():
+        if isinstance(Y, AffineScheme) and Y.coordinate_ring() == X.base_ring():
             return SchemeMorphism_structure_map(self)
         raise NotImplementedError
 
@@ -444,7 +449,7 @@ def __init__(self, X, Y, category=None, check=True, base=ZZ):
             sage: SchemeHomset_points(Spec(QQ), AffineSpace(ZZ,2))
             Set of rational points of Affine Space of dimension 2 over Rational Field
         """
-        if check and not is_AffineScheme(X):
+        if check and not isinstance(X, AffineScheme):
             raise ValueError('The domain must be an affine scheme.')
         SchemeHomset_generic.__init__(self, X, Y, category=category, check=check, base=base)
 
@@ -730,7 +735,7 @@ def value_ring(self):
             Rational Field
         """
         dom = self.domain()
-        if not is_AffineScheme(dom):
+        if not isinstance(dom, AffineScheme):
             raise ValueError("value rings are defined for affine domains only")
         return dom.coordinate_ring()
 
diff --git a/src/sage/schemes/generic/hypersurface.py b/src/sage/schemes/generic/hypersurface.py
index f4991527c78..4d39a7bfc27 100644
--- a/src/sage/schemes/generic/hypersurface.py
+++ b/src/sage/schemes/generic/hypersurface.py
@@ -34,6 +34,9 @@ def is_Hypersurface(self):
         sage: R.<x, y, z> = ZZ[]
         sage: H = ProjectiveHypersurface(x*z + y^2)
         sage: is_Hypersurface(H)
+        doctest:warning...
+        DeprecationWarning: The function is_Hypersurface is deprecated; use 'isinstance(..., (ProjectiveHypersurface, AffineHypersurface))' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
 
     ::
@@ -48,8 +51,11 @@ def is_Hypersurface(self):
         sage: is_Hypersurface(H)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_Hypersurface is deprecated; use 'isinstance(..., (ProjectiveHypersurface, AffineHypersurface))' instead.")
     return isinstance(self, (ProjectiveHypersurface, AffineHypersurface))
 
+
 class ProjectiveHypersurface(AlgebraicScheme_subscheme_projective):
     """
     The projective hypersurface defined by the given polynomial.
diff --git a/src/sage/schemes/generic/scheme.py b/src/sage/schemes/generic/scheme.py
index 2c0e3100c86..7d190275e8e 100644
--- a/src/sage/schemes/generic/scheme.py
+++ b/src/sage/schemes/generic/scheme.py
@@ -44,11 +44,16 @@ def is_Scheme(x):
 
         sage: from sage.schemes.generic.scheme import is_Scheme
         sage: is_Scheme(5)
+        doctest:warning...
+        DeprecationWarning: The function is_Scheme is deprecated; use 'isinstance(..., Scheme)' or categories instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         False
         sage: X = Spec(QQ)
         sage: is_Scheme(X)
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_Scheme is deprecated; use 'isinstance(..., Scheme)' or categories instead.")
     return isinstance(x, Scheme)
 
 
@@ -105,7 +110,7 @@ def __init__(self, X=None, category=None):
 
         if X is None:
             self._base_ring = ZZ
-        elif is_Scheme(X):
+        elif isinstance(X, Scheme):
             self._base_scheme = X
         elif is_SchemeMorphism(X):
             self._base_morphism = X
@@ -255,7 +260,7 @@ def __call__(self, *args):
             S = args[0]
             if S in CommutativeRings():
                 return self.point_homset(S)
-            elif is_Scheme(S):
+            elif isinstance(S, Scheme):
                 return S.Hom(self)
             elif isinstance(S, (list, tuple)):
                 args = S
@@ -331,8 +336,8 @@ def point(self, v, check=True):
             (0 : 0 : 1)
         """
         # todo: update elliptic curve stuff to take point_homset as argument
-        from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
-        if is_EllipticCurve(self):
+        from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
+        if isinstance(self, EllipticCurve_generic):
             try:
                 return self._point(self.point_homset(), v, check=check)
             except AttributeError:  # legacy code without point_homset
@@ -607,7 +612,7 @@ def hom(self, x, Y=None, check=True):
               Defn: Structure map
         """
         if Y is None:
-            if is_Scheme(x):
+            if isinstance(x, Scheme):
                 return self.Hom(x).natural_map()
             else:
                 raise TypeError("unable to determine codomain")
@@ -794,13 +799,19 @@ def is_AffineScheme(x):
 
         sage: from sage.schemes.generic.scheme import is_AffineScheme
         sage: is_AffineScheme(5)
+        doctest:warning...
+        DeprecationWarning: The function is_AffineScheme is deprecated; use 'isinstance(..., AffineScheme)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         False
         sage: E = Spec(QQ)
         sage: is_AffineScheme(E)
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_AffineScheme is deprecated; use 'isinstance(..., AffineScheme)' instead.")
     return isinstance(x, AffineScheme)
 
+
 class AffineScheme(UniqueRepresentation, Scheme):
     """
     Class for general affine schemes.
@@ -1212,7 +1223,7 @@ def hom(self, x, Y=None):
         from sage.categories.map import Map
         from sage.categories.rings import Rings
 
-        if is_Scheme(x):
+        if isinstance(x, Scheme):
             return self.Hom(x).natural_map()
         if Y is None and isinstance(x, Map) and x.category_for().is_subcategory(Rings()):
             # x is a morphism of Rings
diff --git a/src/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py b/src/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py
index c18732064d4..4834152b606 100644
--- a/src/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py
+++ b/src/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py
@@ -51,8 +51,13 @@ def is_HyperellipticCurve(C):
         sage: R.<x> = QQ[]; C = HyperellipticCurve(x^3 + x - 1); C
         Hyperelliptic Curve over Rational Field defined by y^2 = x^3 + x - 1
         sage: is_HyperellipticCurve(C)
+        doctest:warning...
+        DeprecationWarning: The function is_HyperellipticCurve is deprecated; use 'isinstance(..., HyperellipticCurve_generic)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_HyperellipticCurve is deprecated; use 'isinstance(..., HyperellipticCurve_generic)' instead.")
     return isinstance(C, HyperellipticCurve_generic)
 
 
diff --git a/src/sage/schemes/hyperelliptic_curves/jacobian_homset.py b/src/sage/schemes/hyperelliptic_curves/jacobian_homset.py
index a5f4f63876c..88b28a4b753 100644
--- a/src/sage/schemes/hyperelliptic_curves/jacobian_homset.py
+++ b/src/sage/schemes/hyperelliptic_curves/jacobian_homset.py
@@ -161,9 +161,9 @@ def value_ring(self):
         """
         Return S for a homset X(T) where T = Spec(S).
         """
-        from sage.schemes.generic.scheme import is_AffineScheme
+        from sage.schemes.generic.scheme import AffineScheme
         T = self.domain()
-        if is_AffineScheme(T):
+        if isinstance(T, AffineScheme):
             return T.coordinate_ring()
         else:
             raise TypeError("domain of argument must be of the form Spec(S)")
diff --git a/src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py b/src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py
index 03b795a4704..753f83f8b23 100644
--- a/src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py
+++ b/src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py
@@ -74,9 +74,9 @@
 from sage.rings.padics.factory import Qp as pAdicField
 from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.schemes.elliptic_curves.constructor import EllipticCurve
-from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
+from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
 from sage.schemes.hyperelliptic_curves.constructor import HyperellipticCurve
-from sage.schemes.hyperelliptic_curves.hyperelliptic_generic import is_HyperellipticCurve
+from sage.schemes.hyperelliptic_curves.hyperelliptic_generic import HyperellipticCurve_generic
 from sage.structure.element import ModuleElement
 from sage.structure.parent import Parent
 from sage.structure.richcmp import richcmp
@@ -2391,14 +2391,14 @@ def __init__(self, Q, R=None, invert_y=True):
             R = Q.base_ring()
 
         x = PolynomialRing(R, 'xx').gen()
-        if is_EllipticCurve(Q):
+        if isinstance(Q, EllipticCurve_generic):
             E = Q
             if E.a1() != 0 or E.a2() != 0:
                 raise NotImplementedError("curve must be in Weierstrass normal form")
             Q = -E.change_ring(R).defining_polynomial()(x, 0, 1)
             self._curve = E
 
-        elif is_HyperellipticCurve(Q):
+        elif isinstance(Q, HyperellipticCurve_generic):
             C = Q
             if C.hyperelliptic_polynomials()[1] != 0:
                 raise NotImplementedError("curve must be of form y^2 = Q(x)")
diff --git a/src/sage/schemes/jacobians/abstract_jacobian.py b/src/sage/schemes/jacobians/abstract_jacobian.py
index 570c5efaa76..bed9555da46 100644
--- a/src/sage/schemes/jacobians/abstract_jacobian.py
+++ b/src/sage/schemes/jacobians/abstract_jacobian.py
@@ -133,7 +133,7 @@ def __init__(self, C, category=None):
             TypeError: C (=Projective Plane Curve over Ring of integers modulo 6
             defined by x + y + z) must be defined over a field.
         """
-        if not is_Scheme(C):
+        if not isinstance(C, Scheme):
             raise TypeError("Argument (=%s) must be a scheme." % C)
         if C.base_ring() not in _Fields:
             raise TypeError("C (=%s) must be defined over a field." % C)
diff --git a/src/sage/schemes/plane_quartics/quartic_constructor.py b/src/sage/schemes/plane_quartics/quartic_constructor.py
index 37c06a1f5c9..fede02c20bd 100644
--- a/src/sage/schemes/plane_quartics/quartic_constructor.py
+++ b/src/sage/schemes/plane_quartics/quartic_constructor.py
@@ -8,7 +8,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.schemes.projective.projective_space import is_ProjectiveSpace, ProjectiveSpace
+from sage.schemes.projective.projective_space import ProjectiveSpace_ring, ProjectiveSpace
 from sage.rings.polynomial.multi_polynomial import MPolynomial
 
 from .quartic_generic import QuarticCurve_generic
@@ -59,7 +59,7 @@ def QuarticCurve(F, PP=None, check=False):
         raise ValueError("Argument F (=%s) must be a homogeneous polynomial of degree 4" % F)
 
     if PP is not None:
-        if not is_ProjectiveSpace(PP) and PP.dimension == 2:
+        if not isinstance(PP, ProjectiveSpace_ring) and PP.dimension == 2:
             raise ValueError(f"Argument PP (={PP}) must be a projective plane")
     else:
         PP = ProjectiveSpace(P)
diff --git a/src/sage/schemes/plane_quartics/quartic_generic.py b/src/sage/schemes/plane_quartics/quartic_generic.py
index ac2cdd84d82..324ec2f9b13 100644
--- a/src/sage/schemes/plane_quartics/quartic_generic.py
+++ b/src/sage/schemes/plane_quartics/quartic_generic.py
@@ -31,11 +31,17 @@ def is_QuarticCurve(C):
         sage: x,y,z = PolynomialRing(QQ, ['x','y','z']).gens()
         sage: Q = QuarticCurve(x**4 + y**4 + z**4)
         sage: is_QuarticCurve(Q)
+        doctest:warning...
+        DeprecationWarning: The function is_QuarticCurve is deprecated; use 'isinstance(..., QuarticCurve_generic)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
 
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_QuarticCurve is deprecated; use 'isinstance(..., QuarticCurve_generic)' instead.")
     return isinstance(C, QuarticCurve_generic)
 
+
 class QuarticCurve_generic(projective_curve.ProjectivePlaneCurve):
     # DRK: Note that we should check whether the curve is
 
diff --git a/src/sage/schemes/product_projective/homset.py b/src/sage/schemes/product_projective/homset.py
index b0b8655a0ec..32ccb977093 100644
--- a/src/sage/schemes/product_projective/homset.py
+++ b/src/sage/schemes/product_projective/homset.py
@@ -182,8 +182,8 @@ def points(self, **kwds):
         B = kwds.pop('bound', 0)
         X = self.codomain()
 
-        from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
-        if not is_ProductProjectiveSpaces(X) and X.base_ring() in Fields():
+        from sage.schemes.product_projective.space import ProductProjectiveSpaces_ring
+        if not isinstance(X, ProductProjectiveSpaces_ring) and X.base_ring() in Fields():
             # no points
             if X.dimension() == -1:
                 return []
diff --git a/src/sage/schemes/product_projective/morphism.py b/src/sage/schemes/product_projective/morphism.py
index d5b1974164b..30874e5530e 100644
--- a/src/sage/schemes/product_projective/morphism.py
+++ b/src/sage/schemes/product_projective/morphism.py
@@ -112,8 +112,8 @@ def __init__(self, parent, polys, check=True):
 
             target = parent.codomain().ambient_space()
             dom = parent.domain().ambient_space()
-            from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
-            if is_ProductProjectiveSpaces(target):
+            from sage.schemes.product_projective.space import ProductProjectiveSpaces_ring
+            if isinstance(target, ProductProjectiveSpaces_ring):
                 splitpolys = target._factors(polys)
                 for m in range(len(splitpolys)):
                     d = dom._degree(splitpolys[m][0])
diff --git a/src/sage/schemes/product_projective/point.py b/src/sage/schemes/product_projective/point.py
index 6de7cf74d7d..e930a30056b 100644
--- a/src/sage/schemes/product_projective/point.py
+++ b/src/sage/schemes/product_projective/point.py
@@ -537,8 +537,8 @@ def intersection_multiplicity(self, X):
             sage: Q.intersection_multiplicity(Y)                                        # needs sage.libs.singular
             2
         """
-        from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
-        if is_ProductProjectiveSpaces(self.codomain()):
+        from sage.schemes.product_projective.space import ProductProjectiveSpaces_ring
+        if isinstance(self.codomain(), ProductProjectiveSpaces_ring):
             raise TypeError("this point must be a point on a subscheme of a product of projective spaces")
         return self.codomain().intersection_multiplicity(X, self)
 
@@ -565,8 +565,8 @@ def multiplicity(self):
             sage: Q3.multiplicity()                                                     # needs sage.libs.singular
             6
         """
-        from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
-        if is_ProductProjectiveSpaces(self.codomain()):
+        from sage.schemes.product_projective.space import ProductProjectiveSpaces_ring
+        if isinstance(self.codomain(), ProductProjectiveSpaces_ring):
             raise TypeError("this point must be a point on a subscheme of a product of projective spaces")
         return self.codomain().multiplicity(self)
 
diff --git a/src/sage/schemes/product_projective/rational_point.py b/src/sage/schemes/product_projective/rational_point.py
index a4488647063..264e2a4c2d9 100644
--- a/src/sage/schemes/product_projective/rational_point.py
+++ b/src/sage/schemes/product_projective/rational_point.py
@@ -55,8 +55,8 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.schemes.generic.scheme import is_Scheme
-from sage.schemes.product_projective.space import is_ProductProjectiveSpaces
+from sage.schemes.generic.scheme import Scheme
+from sage.schemes.product_projective.space import ProductProjectiveSpaces_ring
 from sage.misc.lazy_import import lazy_import
 from sage.misc.mrange import xmrange
 from sage.misc.misc_c import prod
@@ -124,12 +124,12 @@ def enum_product_projective_rational_field(X, B):
          (0 : 0 : 1 , 0 : 1), (0 : 0 : 1 , 1 : 1), (0 : 1 : 0 , 0 : 1),
          (0 : 1 : 0 , 1 : 1), (1 : -1/2 : 1 , 0 : 1), (1 : -1/2 : 1 , 1 : 1)]
     """
-    if is_Scheme(X):
-        if (not is_ProductProjectiveSpaces(X.ambient_space())):
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), ProductProjectiveSpaces_ring):
             raise TypeError("ambient space must be product of projective space over the rational field")
         X = X(X.base_ring())
     else:
-        if (not is_ProductProjectiveSpaces(X.codomain().ambient_space())):
+        if not isinstance(X.codomain().ambient_space(), ProductProjectiveSpaces_ring):
             raise TypeError("codomain must be product of projective space over the rational field")
 
     R = X.codomain().ambient_space()
@@ -228,12 +228,12 @@ def enum_product_projective_number_field(X, **kwds):
     tol = kwds.pop('tolerance', 1e-2)
     prec = kwds.pop('precision', 53)
 
-    if is_Scheme(X):
-        if (not is_ProductProjectiveSpaces(X.ambient_space())):
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), ProductProjectiveSpaces_ring):
             raise TypeError("ambient space must be product of projective space over the rational field")
         X = X(X.base_ring())
     else:
-        if (not is_ProductProjectiveSpaces(X.codomain().ambient_space())):
+        if not isinstance(X.codomain().ambient_space(), ProductProjectiveSpaces_ring):
             raise TypeError("codomain must be product of projective space over the rational field")
 
     R = X.codomain().ambient_space()
@@ -284,12 +284,12 @@ def enum_product_projective_finite_field(X):
         sage: len(enum_product_projective_finite_field(X))
         36
     """
-    if is_Scheme(X):
-        if (not is_ProductProjectiveSpaces(X.ambient_space())):
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), ProductProjectiveSpaces_ring):
             raise TypeError("ambient space must be product of projective space over the rational field")
         X = X(X.base_ring())
     else:
-        if (not is_ProductProjectiveSpaces(X.codomain().ambient_space())):
+        if not isinstance(X.codomain().ambient_space(), ProductProjectiveSpaces_ring):
             raise TypeError("codomain must be product of projective space over the rational field")
 
     R = X.codomain().ambient_space()
diff --git a/src/sage/schemes/product_projective/space.py b/src/sage/schemes/product_projective/space.py
index 2b4e60905df..ea99ea00559 100644
--- a/src/sage/schemes/product_projective/space.py
+++ b/src/sage/schemes/product_projective/space.py
@@ -73,10 +73,15 @@ def is_ProductProjectiveSpaces(x):
     EXAMPLES::
 
         sage: is_ProductProjectiveSpaces(ProjectiveSpace(5, names='x'))
+        doctest:warning...
+        DeprecationWarning: The function is_ProductProjectiveSpaces is deprecated; use 'isinstance(..., ProductProjectiveSpaces_ring)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         False
         sage: is_ProductProjectiveSpaces(ProductProjectiveSpaces([1, 2, 3], ZZ, 'x'))
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_ProductProjectiveSpaces is deprecated; use 'isinstance(..., ProductProjectiveSpaces_ring)' instead.")
     return isinstance(x, ProductProjectiveSpaces_ring)
 
 
diff --git a/src/sage/schemes/projective/projective_homset.py b/src/sage/schemes/projective/projective_homset.py
index 91c01a51128..5428a101364 100644
--- a/src/sage/schemes/projective/projective_homset.py
+++ b/src/sage/schemes/projective/projective_homset.py
@@ -169,9 +169,9 @@ def points(self, **kwds):
             the numerical fields are inexact;points may be computed partially or incorrectly.
             6
         """
-        from sage.schemes.projective.projective_space import is_ProjectiveSpace
+        from sage.schemes.projective.projective_space import ProjectiveSpace_ring
         X = self.codomain()
-        if not is_ProjectiveSpace(X) and X.base_ring() in Fields():
+        if not isinstance(X, ProjectiveSpace_ring) and X.base_ring() in Fields():
             if hasattr(X.base_ring(), 'precision'):
                 numerical = True
                 verbose("Warning: computations in the numerical fields are inexact;points may be computed partially or incorrectly.", level=0)
@@ -377,7 +377,7 @@ def numerical_points(self, F=None, **kwds):
             ...
             TypeError: F must be a numerical field
         """
-        from sage.schemes.projective.projective_space import is_ProjectiveSpace
+        from sage.schemes.projective.projective_space import ProjectiveSpace_ring
         if F is None:
             F = CC
         if F not in Fields() or not hasattr(F, 'precision'):
@@ -387,7 +387,7 @@ def numerical_points(self, F=None, **kwds):
             raise TypeError('base ring must be a number field')
 
         PP = X.ambient_space().change_ring(F)
-        if not is_ProjectiveSpace(X) and X.base_ring() in Fields():
+        if not isinstance(X, ProjectiveSpace_ring) and X.base_ring() in Fields():
             #Then it must be a subscheme
             dim_ideal = X.defining_ideal().dimension()
             if dim_ideal < 1: # no points
diff --git a/src/sage/schemes/projective/projective_morphism.py b/src/sage/schemes/projective/projective_morphism.py
index a284ecbc585..a21c3f48e17 100644
--- a/src/sage/schemes/projective/projective_morphism.py
+++ b/src/sage/schemes/projective/projective_morphism.py
@@ -1555,8 +1555,8 @@ def wronskian_ideal(self):
         from sage.calculus.functions import jacobian
 
         dom = self.domain()
-        from sage.schemes.projective.projective_space import is_ProjectiveSpace
-        if not (is_ProjectiveSpace(dom) and is_ProjectiveSpace(self.codomain())):
+        from sage.schemes.projective.projective_space import ProjectiveSpace_ring
+        if not (isinstance(dom, ProjectiveSpace_ring) and isinstance(self.codomain(), ProjectiveSpace_ring)):
             raise NotImplementedError("not implemented for subschemes")
         N = dom.dimension_relative() + 1
         R = dom.coordinate_ring()
@@ -1791,9 +1791,9 @@ def _number_field_from_algebraics(self):
                     ((-0.6823278038280193?)*x^3 + (-13)*y^3 : (-14)*y^3)
         """
         from sage.rings.qqbar import number_field_elements_from_algebraics
-        from sage.schemes.projective.projective_space import is_ProjectiveSpace
+        from sage.schemes.projective.projective_space import ProjectiveSpace_ring
 
-        if not (is_ProjectiveSpace(self.domain()) and is_ProjectiveSpace(self.domain())):
+        if not (isinstance(self.domain(), ProjectiveSpace_ring) and isinstance(self.domain(), ProjectiveSpace_ring)):
             raise NotImplementedError("not implemented for subschemes")
 
         K_pre, C, phi = number_field_elements_from_algebraics([c for f in self
diff --git a/src/sage/schemes/projective/projective_point.py b/src/sage/schemes/projective/projective_point.py
index 2f5576e6a12..6aebc66a5e6 100644
--- a/src/sage/schemes/projective/projective_point.py
+++ b/src/sage/schemes/projective/projective_point.py
@@ -1269,8 +1269,8 @@ def _number_field_from_algebraics(self):
             sage: Q[0] == T[0]
             True
         """
-        from sage.schemes.projective.projective_space import is_ProjectiveSpace
-        if not is_ProjectiveSpace(self.codomain()):
+        from sage.schemes.projective.projective_space import ProjectiveSpace_ring
+        if not isinstance(self.codomain(), ProjectiveSpace_ring):
             raise NotImplementedError("not implemented for subschemes")
 
         # Issue #23808: Keep the embedding info associated with the number field K
@@ -1368,8 +1368,8 @@ def intersection_multiplicity(self, X):
             ...
             TypeError: this point must be a point on a projective subscheme
         """
-        from sage.schemes.projective.projective_space import is_ProjectiveSpace
-        if is_ProjectiveSpace(self.codomain()):
+        from sage.schemes.projective.projective_space import ProjectiveSpace_ring
+        if isinstance(self.codomain(), ProjectiveSpace_ring):
             raise TypeError("this point must be a point on a projective subscheme")
         return self.codomain().intersection_multiplicity(X, self)
 
@@ -1393,8 +1393,8 @@ def multiplicity(self):
             sage: Q2.multiplicity()                                                     # needs sage.libs.singular
             8
         """
-        from sage.schemes.projective.projective_space import is_ProjectiveSpace
-        if is_ProjectiveSpace(self.codomain()):
+        from sage.schemes.projective.projective_space import ProjectiveSpace_ring
+        if isinstance(self.codomain(), ProjectiveSpace_ring):
             raise TypeError("this point must be a point on a projective subscheme")
         return self.codomain().multiplicity(self)
 
diff --git a/src/sage/schemes/projective/projective_rational_point.py b/src/sage/schemes/projective/projective_rational_point.py
index 8c2fa76599a..1556ab2d856 100644
--- a/src/sage/schemes/projective/projective_rational_point.py
+++ b/src/sage/schemes/projective/projective_rational_point.py
@@ -63,7 +63,7 @@
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.misc.misc_c import prod
 from sage.misc.mrange import xmrange
-from sage.schemes.generic.scheme import is_Scheme
+from sage.schemes.generic.scheme import Scheme
 from sage.parallel.ncpus import ncpus
 from sage.parallel.use_fork import p_iter_fork
 from sage.matrix.constructor import matrix
@@ -128,12 +128,12 @@ def enum_projective_rational_field(X, B):
 
     - John Cremona and Charlie Turner (06-2010)
     """
-    from sage.schemes.projective.projective_space import is_ProjectiveSpace
-    if is_Scheme(X):
-        if not is_ProjectiveSpace(X.ambient_space()):
+    from sage.schemes.projective.projective_space import ProjectiveSpace_ring
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), ProjectiveSpace_ring):
             raise TypeError("ambient space must be projective space over the rational field")
         X = X(X.base_ring())
-    elif not is_ProjectiveSpace(X.codomain().ambient_space()):
+    elif not isinstance(X.codomain().ambient_space(), ProjectiveSpace_ring):
         raise TypeError("codomain must be projective space over the rational field")
 
     n = X.codomain().ambient_space().ngens()
@@ -206,13 +206,13 @@ def enum_projective_number_field(X, **kwds):
     B = kwds.pop('bound')
     tol = kwds.pop('tolerance', 1e-2)
     prec = kwds.pop('precision', 53)
-    from sage.schemes.projective.projective_space import is_ProjectiveSpace
-    if is_Scheme(X):
-        if (not is_ProjectiveSpace(X.ambient_space())):
+    from sage.schemes.projective.projective_space import ProjectiveSpace_ring
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), ProjectiveSpace_ring):
             raise TypeError("ambient space must be projective space over a number field")
         X = X(X.base_ring())
     else:
-        if (not is_ProjectiveSpace(X.codomain().ambient_space())):
+        if not isinstance(X.codomain().ambient_space(), ProjectiveSpace_ring):
             raise TypeError("codomain must be projective space over a number field")
 
     R = X.codomain().ambient_space()
@@ -287,12 +287,12 @@ def enum_projective_finite_field(X):
 
     - John Cremona and Charlie Turner (06-2010).
     """
-    from sage.schemes.projective.projective_space import is_ProjectiveSpace
-    if is_Scheme(X):
-        if not is_ProjectiveSpace(X.ambient_space()):
+    from sage.schemes.projective.projective_space import ProjectiveSpace_ring
+    if isinstance(X, Scheme):
+        if not isinstance(X.ambient_space(), ProjectiveSpace_ring):
             raise TypeError("ambient space must be projective space over a finite")
         X = X(X.base_ring())
-    elif not is_ProjectiveSpace(X.codomain().ambient_space()):
+    elif not isinstance(X.codomain().ambient_space(), ProjectiveSpace_ring):
         raise TypeError("codomain must be projective space over a finite field")
 
     n = X.codomain().ambient_space().ngens() - 1
diff --git a/src/sage/schemes/projective/projective_space.py b/src/sage/schemes/projective/projective_space.py
index 5c55a62106e..67ddd800ecc 100644
--- a/src/sage/schemes/projective/projective_space.py
+++ b/src/sage/schemes/projective/projective_space.py
@@ -140,12 +140,17 @@ def is_ProjectiveSpace(x):
 
         sage: from sage.schemes.projective.projective_space import is_ProjectiveSpace
         sage: is_ProjectiveSpace(ProjectiveSpace(5, names='x'))
+        doctest:warning...
+        DeprecationWarning: The function is_ProjectiveSpace is deprecated; use 'isinstance(..., ProjectiveSpace_ring)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
         sage: is_ProjectiveSpace(ProjectiveSpace(5, GF(9, 'alpha'), names='x'))         # needs sage.rings.finite_rings
         True
         sage: is_ProjectiveSpace(Spec(ZZ))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_ProjectiveSpace is deprecated; use 'isinstance(..., ProjectiveSpace_ring)' instead.")
     return isinstance(x, ProjectiveSpace_ring)
 
 
@@ -1539,7 +1544,7 @@ def veronese_embedding(self, d, CS=None, order='lex'):
         if CS is None:
             CS = ProjectiveSpace(self.base_ring(), binomial(N + d, d) - 1)
         else:
-            if not is_ProjectiveSpace(CS):
+            if not isinstance(CS, ProjectiveSpace_ring):
                 raise TypeError("(=%s) must be a projective space" % CS)
             if CS.dimension() != binomial(N + d, d) - 1:
                 raise TypeError("(=%s) has the wrong dimension to serve as the codomain space" % CS)
diff --git a/src/sage/schemes/projective/projective_subscheme.py b/src/sage/schemes/projective/projective_subscheme.py
index 3ea963e0e04..b4210db1f21 100644
--- a/src/sage/schemes/projective/projective_subscheme.py
+++ b/src/sage/schemes/projective/projective_subscheme.py
@@ -115,8 +115,8 @@ def point(self, v, check=True):
                 raise ValueError("%s not well defined in dimension > 1" % v)
             v = [1, 0]
         # todo: update elliptic curve stuff to take point_homset as argument
-        from sage.schemes.elliptic_curves.ell_generic import is_EllipticCurve
-        if is_EllipticCurve(self):
+        from sage.schemes.elliptic_curves.ell_generic import EllipticCurve_generic
+        if isinstance(self, EllipticCurve_generic):
             try:
                 return self._point(self.point_homset(), v, check=check)
             except AttributeError:  # legacy code without point_homset
diff --git a/src/sage/schemes/toric/chow_group.py b/src/sage/schemes/toric/chow_group.py
index 482bd5ce81b..d11d70e135b 100644
--- a/src/sage/schemes/toric/chow_group.py
+++ b/src/sage/schemes/toric/chow_group.py
@@ -131,7 +131,7 @@
 from sage.rings.infinity import Infinity
 
 import sage.geometry.abc
-from sage.schemes.toric.variety import is_ToricVariety
+from sage.schemes.toric.variety import ToricVariety_field
 from sage.schemes.toric.divisor import is_ToricDivisor
 
 
@@ -548,7 +548,7 @@ def create_key_and_extra_args(self, toric_variety, base_ring=ZZ, check=True):
             sage: ChowGroup(P2, ZZ, check=True) == ChowGroup(P2, ZZ, check=False)   # indirect doctest
             True
         """
-        if not is_ToricVariety(toric_variety):
+        if not isinstance(toric_variety, ToricVariety_field):
             raise ValueError('first argument must be a toric variety')
 
         if base_ring not in [ZZ, QQ]:
@@ -608,7 +608,7 @@ def __init__(self, toric_variety, base_ring, check):
             sage: P2 = toric_varieties.P2()
             sage: A = ChowGroup_class(P2,ZZ,True); A
             Chow group of 2-d CPR-Fano toric variety covered by 3 affine patches
-            sage: is_ChowGroup(A)
+            sage: isinstance(A, ChowGroup_class)
             True
             sage: is_ChowCycle(A.an_element())
             True
@@ -1216,10 +1216,15 @@ def is_ChowGroup(x) -> bool:
         sage: A = P2.Chow_group()
         sage: from sage.schemes.toric.chow_group import is_ChowGroup
         sage: is_ChowGroup(A)
+        doctest:warning...
+        DeprecationWarning: The function is_ChowGroup is deprecated; use 'isinstance(..., ChowGroup_class)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         True
         sage: is_ChowGroup('Victoria')
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_ChowGroup is deprecated; use 'isinstance(..., ChowGroup_class)' instead.")
     return isinstance(x, ChowGroup_class)
 
 
diff --git a/src/sage/schemes/toric/divisor.py b/src/sage/schemes/toric/divisor.py
index a80d9a41b85..3ec4b2adb62 100644
--- a/src/sage/schemes/toric/divisor.py
+++ b/src/sage/schemes/toric/divisor.py
@@ -185,7 +185,7 @@
 from sage.schemes.generic.divisor import Divisor_generic
 from sage.schemes.generic.divisor_group import DivisorGroup_generic
 from sage.schemes.toric.divisor_class import ToricRationalDivisorClass
-from sage.schemes.toric.variety import CohomologyRing, is_ToricVariety
+from sage.schemes.toric.variety import CohomologyRing, ToricVariety_field
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.element import is_Vector
 
@@ -302,7 +302,7 @@ def ToricDivisor(toric_variety, arg=None, ring=None, check=True, reduce=True):
         ...
         TypeError: cannot deduce coefficient ring for [(u, u)]
     """
-    assert is_ToricVariety(toric_variety)
+    assert isinstance(toric_variety, ToricVariety_field)
 
     # First convert special arguments into lists
     # of multiplicities or (multiplicity,coordinate)
@@ -1687,7 +1687,7 @@ def __init__(self, toric_variety, base_ring):
             sage: DivisorGroup(P2, ZZ) is ToricDivisorGroup(P2, ZZ)
             False
         """
-        assert is_ToricVariety(toric_variety), str(toric_variety) + ' is not a toric variety!'
+        assert isinstance(toric_variety, ToricVariety_field), str(toric_variety) + ' is not a toric variety!'
         super().__init__(toric_variety, base_ring)
 
     def _latex_(self):
diff --git a/src/sage/schemes/toric/fano_variety.py b/src/sage/schemes/toric/fano_variety.py
index d6cbe751274..09014ce20cc 100644
--- a/src/sage/schemes/toric/fano_variety.py
+++ b/src/sage/schemes/toric/fano_variety.py
@@ -170,6 +170,9 @@ def is_CPRFanoToricVariety(x):
 
         sage: from sage.schemes.toric.fano_variety import is_CPRFanoToricVariety
         sage: is_CPRFanoToricVariety(1)
+        doctest:warning...
+        DeprecationWarning: The function is_CPRFanoToricVariety is deprecated; use 'isinstance(..., CPRFanoToricVariety_field)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         False
         sage: FTV = toric_varieties.P2()
         sage: FTV
@@ -179,6 +182,8 @@ def is_CPRFanoToricVariety(x):
         sage: is_CPRFanoToricVariety(ProjectiveSpace(2))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_CPRFanoToricVariety is deprecated; use 'isinstance(..., CPRFanoToricVariety_field)' instead.")
     return isinstance(x, CPRFanoToricVariety_field)
 
 
@@ -1142,7 +1147,7 @@ def cartesian_product(self, other,
             sage: P1xP2.Delta_polar()
             3-d reflexive polytope in 3-d lattice N+N
         """
-        if is_CPRFanoToricVariety(other):
+        if isinstance(other, CPRFanoToricVariety_field):
             fan = self.fan().cartesian_product(other.fan())
             Delta_polar = LatticePolytope(fan.rays())
 
@@ -1314,7 +1319,7 @@ def __init__(self, P_Delta, monomial_points=None, coefficient_names=None,
               s^2*x^2 + s*t*x^2 + t^2*x^2 + s^2*x*y + s*t*x*y
               + t^2*x*y + s^2*y^2 + s*t*y^2 + t^2*y^2
         """
-        if not is_CPRFanoToricVariety(P_Delta):
+        if not isinstance(P_Delta, CPRFanoToricVariety_field):
             raise TypeError("anticanonical hypersurfaces can only be "
                             "constructed for CPR-Fano toric varieties!"
                             "\nGot: %s" % P_Delta)
@@ -1428,7 +1433,7 @@ def __init__(self, P_Delta, nef_partition,
               b1*z1*z2^2 + b2*z2^2*z4 + b5*z1*z2*z5
               + b4*z2*z4*z5 + b3*z1*z5^2 + b0*z4*z5^2
         """
-        if not is_CPRFanoToricVariety(P_Delta):
+        if not isinstance(P_Delta, CPRFanoToricVariety_field):
             raise TypeError("nef complete intersections can only be "
                             "constructed for CPR-Fano toric varieties!"
                             "\nGot: %s" % P_Delta)
diff --git a/src/sage/schemes/toric/homset.py b/src/sage/schemes/toric/homset.py
index e02d0b92078..80a879a6aed 100644
--- a/src/sage/schemes/toric/homset.py
+++ b/src/sage/schemes/toric/homset.py
@@ -166,8 +166,8 @@ def __init__(self, X, Y, category=None, check=True, base=ZZ):
                     to Rational polyhedral fan in 1-d lattice N.
         """
         SchemeHomset_generic.__init__(self, X, Y, category=category, check=check, base=base)
-        from sage.schemes.toric.variety import is_ToricVariety
-        if is_ToricVariety(X) and is_ToricVariety(Y):
+        from sage.schemes.toric.variety import ToricVariety_field
+        if isinstance(X, ToricVariety_field) and isinstance(Y, ToricVariety_field):
             self.register_conversion(MatrixSpace(ZZ, X.fan().dim(), Y.fan().dim()))
 
     def _element_constructor_(self, x, check=True):
diff --git a/src/sage/schemes/toric/morphism.py b/src/sage/schemes/toric/morphism.py
index c22f88e99fb..a7afee25f30 100644
--- a/src/sage/schemes/toric/morphism.py
+++ b/src/sage/schemes/toric/morphism.py
@@ -374,7 +374,7 @@
 from sage.geometry.cone import Cone
 from sage.geometry.fan import Fan
 
-from sage.schemes.generic.scheme import is_Scheme
+from sage.schemes.generic.scheme import Scheme
 from sage.schemes.generic.morphism import (
     is_SchemeMorphism,
     SchemeMorphism, SchemeMorphism_point, SchemeMorphism_polynomial
@@ -425,7 +425,7 @@ def __init__(self, X, coordinates, check=True):
             [1 : 2 : 3 : 4]
         """
         # Convert scheme to its set of points over the base ring
-        if is_Scheme(X):
+        if isinstance(X, Scheme):
             X = X(X.base_ring())
         super().__init__(X)
         if check:
diff --git a/src/sage/schemes/toric/sheaf/constructor.py b/src/sage/schemes/toric/sheaf/constructor.py
index 0fb0c0a34e5..3b23c4d9213 100644
--- a/src/sage/schemes/toric/sheaf/constructor.py
+++ b/src/sage/schemes/toric/sheaf/constructor.py
@@ -13,7 +13,7 @@
 #  the License, or (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
-from sage.schemes.toric.variety import is_ToricVariety
+from sage.schemes.toric.variety import ToricVariety_field
 from sage.modules.filtered_vector_space import FilteredVectorSpace
 
 
@@ -36,7 +36,7 @@ def TangentBundle(X):
         sage: TangentBundle(dP7)
         Rank 2 bundle on 2-d CPR-Fano toric variety covered by 5 affine patches.
     """
-    if not is_ToricVariety(X):
+    if not isinstance(X, ToricVariety_field):
         raise ValueError('not a toric variety')
 
     fan = X.fan()
@@ -94,7 +94,7 @@ def TrivialBundle(X, rank=1):
         sage: I3.cohomology(weight=(0,0), dim=True)
         (3, 0, 0)
     """
-    if not is_ToricVariety(X):
+    if not isinstance(X, ToricVariety_field):
         raise ValueError('not a toric variety')
 
     base_ring = X.base_ring()
@@ -127,7 +127,7 @@ def LineBundle(X, D):
         sage: O_D.cohomology(dim=True, weight=(0,0))
         (1, 0, 0)
     """
-    if not is_ToricVariety(X):
+    if not isinstance(X, ToricVariety_field):
         raise ValueError('not a toric variety')
 
     base_ring = X.base_ring()
diff --git a/src/sage/schemes/toric/sheaf/klyachko.py b/src/sage/schemes/toric/sheaf/klyachko.py
index 4325e77f186..b6c7147140c 100644
--- a/src/sage/schemes/toric/sheaf/klyachko.py
+++ b/src/sage/schemes/toric/sheaf/klyachko.py
@@ -69,8 +69,13 @@ def is_KlyachkoBundle(X):
 
         sage: from sage.schemes.toric.sheaf.klyachko import is_KlyachkoBundle
         sage: is_KlyachkoBundle('test')
+        doctest:warning...
+        DeprecationWarning: The function is_KlyachkoBundle is deprecated; use 'isinstance(..., KlyachkoBundle_class)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_KlyachkoBundle is deprecated; use 'isinstance(..., KlyachkoBundle_class)' instead.")
     return isinstance(X, KlyachkoBundle_class)
 
 
diff --git a/src/sage/schemes/toric/variety.py b/src/sage/schemes/toric/variety.py
index 6a6a8d3252a..b978ede251d 100644
--- a/src/sage/schemes/toric/variety.py
+++ b/src/sage/schemes/toric/variety.py
@@ -351,6 +351,9 @@ def is_ToricVariety(x):
 
         sage: from sage.schemes.toric.variety import is_ToricVariety
         sage: is_ToricVariety(1)
+        doctest:warning...
+        DeprecationWarning: The function is_ToricVariety is deprecated; use 'isinstance(..., ToricVariety_field)' instead.
+        See https://github.com/sagemath/sage/issues/38022 for details.
         False
         sage: fan = FaceFan(lattice_polytope.cross_polytope(2))
         sage: P = ToricVariety(fan)
@@ -361,6 +364,8 @@ def is_ToricVariety(x):
         sage: is_ToricVariety(ProjectiveSpace(2))
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38022, "The function is_ToricVariety is deprecated; use 'isinstance(..., ToricVariety_field)' instead.")
     return isinstance(x, ToricVariety_field)
 
 
@@ -1339,7 +1344,7 @@ def is_isomorphic(self, another):
         """
         if self is another:
             return True
-        if not is_ToricVariety(another):
+        if not isinstance(another, ToricVariety_field):
             raise TypeError(
                 "only another toric variety can be checked for isomorphism; "
                 "got %s" % another)