algebraic_geometry.morphisms.finite_type
⟷
Mathlib.AlgebraicGeometry.Morphisms.FiniteType
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
-import Mathbin.AlgebraicGeometry.Morphisms.RingHomProperties
-import Mathbin.RingTheory.RingHom.FiniteType
+import AlgebraicGeometry.Morphisms.RingHomProperties
+import RingTheory.RingHom.FiniteType
#align_import algebraic_geometry.morphisms.finite_type from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebraic_geometry.morphisms.finite_type
-! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.AlgebraicGeometry.Morphisms.RingHomProperties
import Mathbin.RingTheory.RingHom.FiniteType
+#align_import algebraic_geometry.morphisms.finite_type from "leanprover-community/mathlib"@"08b081ea92d80e3a41f899eea36ef6d56e0f1db0"
+
/-!
# Morphisms of finite type
mathlib commit https://github.com/leanprover-community/mathlib/commit/bf2428c9486c407ca38b5b3fb10b87dad0bc99fa
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
! This file was ported from Lean 3 source module algebraic_geometry.morphisms.finite_type
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 08b081ea92d80e3a41f899eea36ef6d56e0f1db0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.RingHom.FiniteType
/-!
# Morphisms of finite type
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
A morphism of schemes `f : X ⟶ Y` is locally of finite type if for each affine `U ⊆ Y` and
`V ⊆ f ⁻¹' U`, The induced map `Γ(Y, U) ⟶ Γ(X, V)` is of finite type.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372
@@ -34,6 +34,7 @@ namespace AlgebraicGeometry
variable {X Y : Scheme.{u}} (f : X ⟶ Y)
+#print AlgebraicGeometry.LocallyOfFiniteType /-
/-- A morphism of schemes `f : X ⟶ Y` is locally of finite type if for each affine `U ⊆ Y` and
`V ⊆ f ⁻¹' U`, The induced map `Γ(Y, U) ⟶ Γ(X, V)` is of finite type.
-/
@@ -43,29 +44,39 @@ class LocallyOfFiniteType (f : X ⟶ Y) : Prop where
∀ (U : Y.affineOpens) (V : X.affineOpens) (e : V.1 ≤ (Opens.map f.1.base).obj U.1),
(f.appLe e).FiniteType
#align algebraic_geometry.locally_of_finite_type AlgebraicGeometry.LocallyOfFiniteType
+-/
+#print AlgebraicGeometry.locallyOfFiniteType_eq /-
theorem locallyOfFiniteType_eq : @LocallyOfFiniteType = affineLocally @RingHom.FiniteType :=
by
ext X Y f
rw [locally_of_finite_type_iff, affine_locally_iff_affine_opens_le]
exact RingHom.finiteType_respectsIso
#align algebraic_geometry.locally_of_finite_type_eq AlgebraicGeometry.locallyOfFiniteType_eq
+-/
+#print AlgebraicGeometry.locallyOfFiniteTypeOfIsOpenImmersion /-
instance (priority := 900) locallyOfFiniteTypeOfIsOpenImmersion {X Y : Scheme} (f : X ⟶ Y)
[IsOpenImmersionCat f] : LocallyOfFiniteType f :=
- locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersionCat f
+ locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersion f
#align algebraic_geometry.locally_of_finite_type_of_is_open_immersion AlgebraicGeometry.locallyOfFiniteTypeOfIsOpenImmersion
+-/
+#print AlgebraicGeometry.locallyOfFiniteType_stableUnderComposition /-
theorem locallyOfFiniteType_stableUnderComposition :
MorphismProperty.StableUnderComposition @LocallyOfFiniteType :=
locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_stableUnderComposition
#align algebraic_geometry.locally_of_finite_type_stable_under_composition AlgebraicGeometry.locallyOfFiniteType_stableUnderComposition
+-/
+#print AlgebraicGeometry.locallyOfFiniteTypeComp /-
instance locallyOfFiniteTypeComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
[hf : LocallyOfFiniteType f] [hg : LocallyOfFiniteType g] : LocallyOfFiniteType (f ≫ g) :=
locallyOfFiniteType_stableUnderComposition f g hf hg
#align algebraic_geometry.locally_of_finite_type_comp AlgebraicGeometry.locallyOfFiniteTypeComp
+-/
+#print AlgebraicGeometry.locallyOfFiniteTypeOfComp /-
theorem locallyOfFiniteTypeOfComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
[hf : LocallyOfFiniteType (f ≫ g)] : LocallyOfFiniteType f :=
by
@@ -75,29 +86,38 @@ theorem locallyOfFiniteTypeOfComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
introv H
exact RingHom.FiniteType.of_comp_finiteType H
#align algebraic_geometry.locally_of_finite_type_of_comp AlgebraicGeometry.locallyOfFiniteTypeOfComp
+-/
+#print AlgebraicGeometry.LocallyOfFiniteType.affine_openCover_iff /-
theorem LocallyOfFiniteType.affine_openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y)
(𝒰 : Scheme.OpenCover.{u} Y) [∀ i, IsAffine (𝒰.obj i)]
(𝒰' : ∀ i, Scheme.OpenCover.{u} ((𝒰.pullbackCover f).obj i)) [∀ i j, IsAffine ((𝒰' i).obj j)] :
LocallyOfFiniteType f ↔ ∀ i j, (Scheme.Γ.map ((𝒰' i).map j ≫ pullback.snd).op).FiniteType :=
locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affine_openCover_iff f 𝒰 𝒰'
#align algebraic_geometry.locally_of_finite_type.affine_open_cover_iff AlgebraicGeometry.LocallyOfFiniteType.affine_openCover_iff
+-/
+#print AlgebraicGeometry.LocallyOfFiniteType.source_openCover_iff /-
theorem LocallyOfFiniteType.source_openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y)
(𝒰 : Scheme.OpenCover.{u} X) : LocallyOfFiniteType f ↔ ∀ i, LocallyOfFiniteType (𝒰.map i ≫ f) :=
locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.source_openCover_iff f 𝒰
#align algebraic_geometry.locally_of_finite_type.source_open_cover_iff AlgebraicGeometry.LocallyOfFiniteType.source_openCover_iff
+-/
+#print AlgebraicGeometry.LocallyOfFiniteType.openCover_iff /-
theorem LocallyOfFiniteType.openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y)
(𝒰 : Scheme.OpenCover.{u} Y) :
LocallyOfFiniteType f ↔ ∀ i, LocallyOfFiniteType (pullback.snd : pullback f (𝒰.map i) ⟶ _) :=
locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.is_local_affineLocally.openCover_iff f 𝒰
#align algebraic_geometry.locally_of_finite_type.open_cover_iff AlgebraicGeometry.LocallyOfFiniteType.openCover_iff
+-/
+#print AlgebraicGeometry.locallyOfFiniteType_respectsIso /-
theorem locallyOfFiniteType_respectsIso : MorphismProperty.RespectsIso @LocallyOfFiniteType :=
locallyOfFiniteType_eq.symm ▸
targetAffineLocally_respectsIso (sourceAffineLocally_respectsIso RingHom.finiteType_respectsIso)
#align algebraic_geometry.locally_of_finite_type_respects_iso AlgebraicGeometry.locallyOfFiniteType_respectsIso
+-/
end AlgebraicGeometry
mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8
@@ -91,7 +91,7 @@ theorem LocallyOfFiniteType.source_openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y
theorem LocallyOfFiniteType.openCover_iff {X Y : Scheme.{u}} (f : X ⟶ Y)
(𝒰 : Scheme.OpenCover.{u} Y) :
LocallyOfFiniteType f ↔ ∀ i, LocallyOfFiniteType (pullback.snd : pullback f (𝒰.map i) ⟶ _) :=
- locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.isLocalAffineLocally.openCover_iff f 𝒰
+ locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.is_local_affineLocally.openCover_iff f 𝒰
#align algebraic_geometry.locally_of_finite_type.open_cover_iff AlgebraicGeometry.LocallyOfFiniteType.openCover_iff
theorem locallyOfFiniteType_respectsIso : MorphismProperty.RespectsIso @LocallyOfFiniteType :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb
@@ -52,8 +52,8 @@ theorem locallyOfFiniteType_eq : @LocallyOfFiniteType = affineLocally @RingHom.F
#align algebraic_geometry.locally_of_finite_type_eq AlgebraicGeometry.locallyOfFiniteType_eq
instance (priority := 900) locallyOfFiniteTypeOfIsOpenImmersion {X Y : Scheme} (f : X ⟶ Y)
- [IsOpenImmersion f] : LocallyOfFiniteType f :=
- locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersion f
+ [IsOpenImmersionCat f] : LocallyOfFiniteType f :=
+ locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersionCat f
#align algebraic_geometry.locally_of_finite_type_of_is_open_immersion AlgebraicGeometry.locallyOfFiniteTypeOfIsOpenImmersion
theorem locallyOfFiniteType_stableUnderComposition :
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -46,7 +46,7 @@ class LocallyOfFiniteType (f : X ⟶ Y) : Prop where
theorem locallyOfFiniteType_eq : @LocallyOfFiniteType = affineLocally @RingHom.FiniteType :=
by
- ext (X Y f)
+ ext X Y f
rw [locally_of_finite_type_iff, affine_locally_iff_affine_opens_le]
exact RingHom.finiteType_respectsIso
#align algebraic_geometry.locally_of_finite_type_eq AlgebraicGeometry.locallyOfFiniteType_eq
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
The type class MorphismProperty.HasTwoOutOfThreeProperty
is introduced. The structure StableUnderComposition
is also changed into a type class IsStableUnderComposition
.
Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
@@ -52,14 +52,14 @@ instance (priority := 900) locallyOfFiniteTypeOfIsOpenImmersion {X Y : Scheme} (
locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_of_isOpenImmersion f
#align algebraic_geometry.locally_of_finite_type_of_is_open_immersion AlgebraicGeometry.locallyOfFiniteTypeOfIsOpenImmersion
-theorem locallyOfFiniteType_stableUnderComposition :
- MorphismProperty.StableUnderComposition @LocallyOfFiniteType :=
- locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_stableUnderComposition
-#align algebraic_geometry.locally_of_finite_type_stable_under_composition AlgebraicGeometry.locallyOfFiniteType_stableUnderComposition
+instance locallyOfFiniteType_isStableUnderComposition :
+ MorphismProperty.IsStableUnderComposition @LocallyOfFiniteType :=
+ locallyOfFiniteType_eq.symm ▸ RingHom.finiteType_is_local.affineLocally_isStableUnderComposition
+#align algebraic_geometry.locally_of_finite_type_stable_under_composition AlgebraicGeometry.locallyOfFiniteType_isStableUnderComposition
instance locallyOfFiniteTypeComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
[hf : LocallyOfFiniteType f] [hg : LocallyOfFiniteType g] : LocallyOfFiniteType (f ≫ g) :=
- locallyOfFiniteType_stableUnderComposition f g hf hg
+ MorphismProperty.comp_mem _ f g hf hg
#align algebraic_geometry.locally_of_finite_type_comp AlgebraicGeometry.locallyOfFiniteTypeComp
theorem locallyOfFiniteTypeOfComp {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
@@ -95,4 +95,3 @@ theorem locallyOfFiniteType_respectsIso : MorphismProperty.RespectsIso @LocallyO
#align algebraic_geometry.locally_of_finite_type_respects_iso AlgebraicGeometry.locallyOfFiniteType_respectsIso
end AlgebraicGeometry
-
@@ -43,7 +43,7 @@ class LocallyOfFiniteType (f : X ⟶ Y) : Prop where
theorem locallyOfFiniteType_eq : @LocallyOfFiniteType = affineLocally @RingHom.FiniteType := by
ext X Y f
- rw [LocallyOfFiniteType_iff, affineLocally_iff_affineOpens_le]
+ rw [locallyOfFiniteType_iff, affineLocally_iff_affineOpens_le]
exact RingHom.finiteType_respectsIso
#align algebraic_geometry.locally_of_finite_type_eq AlgebraicGeometry.locallyOfFiniteType_eq
@@ -2,15 +2,12 @@
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebraic_geometry.morphisms.finite_type
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties
import Mathlib.RingTheory.RingHom.FiniteType
+#align_import algebraic_geometry.morphisms.finite_type from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
/-!
# Morphisms of finite type
Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Matthew Robert Ballard <100034030+mattrobball@users.noreply.github.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
The unported dependencies are