algebraic_geometry.Scheme | Mathlib porting status

Changes since the initial port

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.

Changes in mathlib3

88474d1b

(last sync)

chore(algebraic_geometry/Scheme): remove @[simps] from Spec (#19188)

The @[simps] on Spec produces lemmas that aren't needed in mathlib3, and get in the way in mathlib4. This backports the removal of this attribute, to match https://github.com/leanprover-community/mathlib4/pull/5040.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

Diff

@@ -158,7 +158,11 @@ Spec.LocallyRingedSpace_map_comp f g
 /--
 The spectrum, as a contravariant functor from commutative rings to schemes.
 -/
-@[simps] def Spec : CommRingᵒᵖ ⥤ Scheme :=
+-- TODO: make either `Spec_obj` or `Spec.obj` the simp-normal form. `LocallyRingedSpace_obj` is
+-- the simp-normal form of `toLocallyRingedSpace.obj`, but adding `simps` here without `attrs := []`
+-- for the same effect caused problems in mathlib4.
+@[simps {attrs := []}]
+def Spec : CommRingᵒᵖ ⥤ Scheme :=
 { obj := λ R, Spec_obj (unop R),
   map := λ R S f, Spec_map f.unop,
   map_id' := λ R, by rw [unop_id, Spec_map_id],

06c75afe

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

88474d1b

bump to nightly-2024-04-14-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

f736ea6b

Diff

@@ -81,7 +81,7 @@ protected abbrev sheaf (X : Scheme) :=
 @[simps]
 def forgetToLocallyRingedSpace : Scheme ⥤ LocallyRingedSpace :=
   inducedFunctor _
-deriving Full, Faithful
+deriving CategoryTheory.Functor.Full, CategoryTheory.Functor.Faithful
 #align algebraic_geometry.Scheme.forget_to_LocallyRingedSpace AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
 -/

88474d1b

bump to nightly-2024-02-05-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

516c6ec2

Diff

@@ -36,7 +36,7 @@ open Opposite
 namespace AlgebraicGeometry
 
 #print AlgebraicGeometry.Scheme /-
-/- ./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:429:11: unsupported: advanced extends in structure -/
 /-- We define `Scheme` as a `X : LocallyRingedSpace`,
 along with a proof that every point has an open neighbourhood `U`
 so that that the restriction of `X` to `U` is isomorphic,
@@ -44,7 +44,7 @@ as a locally ringed space, to `Spec.to_LocallyRingedSpace.obj (op R)`
 for some `R : CommRing`.
 -/
 structure Scheme extends
-    "./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure" where
+    "./././Mathport/Syntax/Translate/Command.lean:429:11: unsupported: advanced extends in structure" where
   local_affine :
     ∀ x : to_LocallyRingedSpace,
       ∃ (U : OpenNhds x) (R : CommRingCat),

88474d1b

bump to nightly-2023-12-23-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

b8c74971

Diff

@@ -36,7 +36,7 @@ open Opposite
 namespace AlgebraicGeometry
 
 #print AlgebraicGeometry.Scheme /-
-/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure -/
 /-- We define `Scheme` as a `X : LocallyRingedSpace`,
 along with a proof that every point has an open neighbourhood `U`
 so that that the restriction of `X` to `U` is isomorphic,
@@ -44,7 +44,7 @@ as a locally ringed space, to `Spec.to_LocallyRingedSpace.obj (op R)`
 for some `R : CommRing`.
 -/
 structure Scheme extends
-    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure" where
+    "./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure" where
   local_affine :
     ∀ x : to_LocallyRingedSpace,
       ∃ (U : OpenNhds x) (R : CommRingCat),

88474d1b

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.AlgebraicGeometry.Spec
-import Mathbin.Algebra.Category.Ring.Constructions
+import AlgebraicGeometry.Spec
+import Algebra.Category.Ring.Constructions
 
 #align_import algebraic_geometry.Scheme from "leanprover-community/mathlib"@"88474d1b5af6d37c2ab728b757771bced7f5194c"
 
@@ -36,7 +36,7 @@ open Opposite
 namespace AlgebraicGeometry
 
 #print AlgebraicGeometry.Scheme /-
-/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
 /-- We define `Scheme` as a `X : LocallyRingedSpace`,
 along with a proof that every point has an open neighbourhood `U`
 so that that the restriction of `X` to `U` is isomorphic,
@@ -44,7 +44,7 @@ as a locally ringed space, to `Spec.to_LocallyRingedSpace.obj (op R)`
 for some `R : CommRing`.
 -/
 structure Scheme extends
-    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure" where
+    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure" where
   local_affine :
     ∀ x : to_LocallyRingedSpace,
       ∃ (U : OpenNhds x) (R : CommRingCat),

88474d1b

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebraic_geometry.Scheme
-! leanprover-community/mathlib commit 88474d1b5af6d37c2ab728b757771bced7f5194c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicGeometry.Spec
 import Mathbin.Algebra.Category.Ring.Constructions
 
+#align_import algebraic_geometry.Scheme from "leanprover-community/mathlib"@"88474d1b5af6d37c2ab728b757771bced7f5194c"
+
 /-!
 # The category of schemes

88474d1b

bump to nightly-2023-06-18-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

3b5e23dc

Diff

@@ -38,6 +38,7 @@ open Opposite
 
 namespace AlgebraicGeometry
 
+#print AlgebraicGeometry.Scheme /-
 /- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
 /-- We define `Scheme` as a `X : LocallyRingedSpace`,
 along with a proof that every point has an open neighbourhood `U`
@@ -53,84 +54,110 @@ structure Scheme extends
         Nonempty
           (to_LocallyRingedSpace.restrict U.OpenEmbedding ≅ Spec.toLocallyRingedSpace.obj (op R))
 #align algebraic_geometry.Scheme AlgebraicGeometry.Scheme
+-/
 
 namespace Scheme
 
+#print AlgebraicGeometry.Scheme.Hom /-
 -- There isn't nessecarily a morphism between two schemes.
 /-- A morphism between schemes is a morphism between the underlying locally ringed spaces. -/
 @[nolint has_nonempty_instance]
 def Hom (X Y : Scheme) : Type _ :=
   X.toLocallyRingedSpace ⟶ Y.toLocallyRingedSpace
 #align algebraic_geometry.Scheme.hom AlgebraicGeometry.Scheme.Hom
+-/
 
 /-- Schemes are a full subcategory of locally ringed spaces.
 -/
 instance : Category Scheme :=
   { InducedCategory.category Scheme.toLocallyRingedSpace with Hom := Hom }
 
+#print AlgebraicGeometry.Scheme.sheaf /-
 /-- The structure sheaf of a Scheme. -/
 protected abbrev sheaf (X : Scheme) :=
   X.toSheafedSpace.Sheaf
 #align algebraic_geometry.Scheme.sheaf AlgebraicGeometry.Scheme.sheaf
+-/
 
+#print AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace /-
 /-- The forgetful functor from `Scheme` to `LocallyRingedSpace`. -/
 @[simps]
 def forgetToLocallyRingedSpace : Scheme ⥤ LocallyRingedSpace :=
   inducedFunctor _
 deriving Full, Faithful
 #align algebraic_geometry.Scheme.forget_to_LocallyRingedSpace AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
+-/
 
+#print AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace_preimage /-
 @[simp]
 theorem forgetToLocallyRingedSpace_preimage {X Y : Scheme} (f : X ⟶ Y) :
     Scheme.forgetToLocallyRingedSpace.preimage f = f :=
   rfl
 #align algebraic_geometry.Scheme.forget_to_LocallyRingedSpace_preimage AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace_preimage
+-/
 
+#print AlgebraicGeometry.Scheme.forgetToTop /-
 /-- The forgetful functor from `Scheme` to `Top`. -/
 @[simps]
 def forgetToTop : Scheme ⥤ TopCat :=
   Scheme.forgetToLocallyRingedSpace ⋙ LocallyRingedSpace.forgetToTop
 #align algebraic_geometry.Scheme.forget_to_Top AlgebraicGeometry.Scheme.forgetToTop
+-/
 
+#print AlgebraicGeometry.Scheme.id_val_base /-
 @[simp]
 theorem id_val_base (X : Scheme) : (𝟙 X : _).1.base = 𝟙 _ :=
   rfl
 #align algebraic_geometry.Scheme.id_val_base AlgebraicGeometry.Scheme.id_val_base
+-/
 
+#print AlgebraicGeometry.Scheme.id_app /-
 @[simp]
 theorem id_app {X : Scheme} (U : (Opens X.carrier)ᵒᵖ) :
     (𝟙 X : _).val.c.app U =
       X.Presheaf.map (eqToHom (by induction U using Opposite.rec'; cases U; rfl)) :=
   PresheafedSpace.id_c_app X.toPresheafedSpace U
 #align algebraic_geometry.Scheme.id_app AlgebraicGeometry.Scheme.id_app
+-/
 
+#print AlgebraicGeometry.Scheme.comp_val /-
 @[reassoc]
 theorem comp_val {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g).val = f.val ≫ g.val :=
   rfl
 #align algebraic_geometry.Scheme.comp_val AlgebraicGeometry.Scheme.comp_val
+-/
 
+#print AlgebraicGeometry.Scheme.comp_coeBase /-
 @[reassoc, simp]
 theorem comp_coeBase {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).val.base = f.val.base ≫ g.val.base :=
   rfl
 #align algebraic_geometry.Scheme.comp_coe_base AlgebraicGeometry.Scheme.comp_coeBase
+-/
 
+#print AlgebraicGeometry.Scheme.comp_val_base /-
 @[reassoc, elementwise]
 theorem comp_val_base {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).val.base = f.val.base ≫ g.val.base :=
   rfl
 #align algebraic_geometry.Scheme.comp_val_base AlgebraicGeometry.Scheme.comp_val_base
+-/
 
+#print AlgebraicGeometry.Scheme.comp_val_c_app /-
 @[reassoc, simp]
 theorem comp_val_c_app {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (f ≫ g).val.c.app U = g.val.c.app U ≫ f.val.c.app _ :=
   rfl
 #align algebraic_geometry.Scheme.comp_val_c_app AlgebraicGeometry.Scheme.comp_val_c_app
+-/
 
+#print AlgebraicGeometry.Scheme.congr_app /-
 theorem congr_app {X Y : Scheme} {f g : X ⟶ Y} (e : f = g) (U) :
     f.val.c.app U = g.val.c.app U ≫ X.Presheaf.map (eqToHom (by subst e)) := by subst e; dsimp; simp
 #align algebraic_geometry.Scheme.congr_app AlgebraicGeometry.Scheme.congr_app
+-/
 
+#print AlgebraicGeometry.Scheme.app_eq /-
 theorem app_eq {X Y : Scheme} (f : X ⟶ Y) {U V : Opens Y.carrier} (e : U = V) :
     f.val.c.app (op U) =
       Y.Presheaf.map (eqToHom e.symm).op ≫
@@ -139,12 +166,16 @@ theorem app_eq {X Y : Scheme} (f : X ⟶ Y) {U V : Opens Y.carrier} (e : U = V)
   rw [← is_iso.inv_comp_eq, ← functor.map_inv, f.val.c.naturality, presheaf.pushforward_obj_map]
   congr
 #align algebraic_geometry.Scheme.app_eq AlgebraicGeometry.Scheme.app_eq
+-/
 
+#print AlgebraicGeometry.Scheme.is_locallyRingedSpace_iso /-
 instance is_locallyRingedSpace_iso {X Y : Scheme} (f : X ⟶ Y) [IsIso f] :
     @IsIso LocallyRingedSpace _ _ _ f :=
   forgetToLocallyRingedSpace.map_isIso f
 #align algebraic_geometry.Scheme.is_LocallyRingedSpace_iso AlgebraicGeometry.Scheme.is_locallyRingedSpace_iso
+-/
 
+#print AlgebraicGeometry.Scheme.inv_val_c_app /-
 @[simp]
 theorem inv_val_c_app {X Y : Scheme} (f : X ⟶ Y) [IsIso f] (U : Opens X.carrier) :
     (inv f).val.c.app (op U) =
@@ -159,14 +190,18 @@ theorem inv_val_c_app {X Y : Scheme} (f : X ⟶ Y) [IsIso f] (U : Opens X.carrie
     eq_to_hom_op]
   rfl
 #align algebraic_geometry.Scheme.inv_val_c_app AlgebraicGeometry.Scheme.inv_val_c_app
+-/
 
+#print AlgebraicGeometry.Scheme.Hom.appLe /-
 /-- Given a morphism of schemes `f : X ⟶ Y`, and open sets `U ⊆ Y`, `V ⊆ f ⁻¹' U`,
 this is the induced map `Γ(Y, U) ⟶ Γ(X, V)`. -/
 abbrev Hom.appLe {X Y : Scheme} (f : X ⟶ Y) {V : Opens X.carrier} {U : Opens Y.carrier}
     (e : V ≤ (Opens.map f.1.base).obj U) : Y.Presheaf.obj (op U) ⟶ X.Presheaf.obj (op V) :=
   f.1.c.app (op U) ≫ X.Presheaf.map (homOfLE e).op
 #align algebraic_geometry.Scheme.hom.app_le AlgebraicGeometry.Scheme.Hom.appLe
+-/
 
+#print AlgebraicGeometry.Scheme.specObj /-
 /-- The spectrum of a commutative ring, as a scheme.
 -/
 def specObj (R : CommRingCat) : Scheme
@@ -174,42 +209,54 @@ def specObj (R : CommRingCat) : Scheme
   local_affine x := ⟨⟨⊤, trivial⟩, R, ⟨(Spec.toLocallyRingedSpace.obj (op R)).restrictTopIso⟩⟩
   toLocallyRingedSpace := Spec.locallyRingedSpaceObj R
 #align algebraic_geometry.Scheme.Spec_obj AlgebraicGeometry.Scheme.specObj
+-/
 
+#print AlgebraicGeometry.Scheme.specObj_toLocallyRingedSpace /-
 @[simp]
 theorem specObj_toLocallyRingedSpace (R : CommRingCat) :
     (specObj R).toLocallyRingedSpace = Spec.locallyRingedSpaceObj R :=
   rfl
 #align algebraic_geometry.Scheme.Spec_obj_to_LocallyRingedSpace AlgebraicGeometry.Scheme.specObj_toLocallyRingedSpace
+-/
 
+#print AlgebraicGeometry.Scheme.specMap /-
 /-- The induced map of a ring homomorphism on the ring spectra, as a morphism of schemes.
 -/
 def specMap {R S : CommRingCat} (f : R ⟶ S) : specObj S ⟶ specObj R :=
   (Spec.locallyRingedSpaceMap f : Spec.locallyRingedSpaceObj S ⟶ Spec.locallyRingedSpaceObj R)
 #align algebraic_geometry.Scheme.Spec_map AlgebraicGeometry.Scheme.specMap
+-/
 
+#print AlgebraicGeometry.Scheme.specMap_id /-
 @[simp]
 theorem specMap_id (R : CommRingCat) : specMap (𝟙 R) = 𝟙 (specObj R) :=
   Spec.locallyRingedSpaceMap_id R
 #align algebraic_geometry.Scheme.Spec_map_id AlgebraicGeometry.Scheme.specMap_id
+-/
 
+#print AlgebraicGeometry.Scheme.specMap_comp /-
 theorem specMap_comp {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T) :
     specMap (f ≫ g) = specMap g ≫ specMap f :=
   Spec.locallyRingedSpaceMap_comp f g
 #align algebraic_geometry.Scheme.Spec_map_comp AlgebraicGeometry.Scheme.specMap_comp
+-/
 
+#print AlgebraicGeometry.Scheme.Spec /-
 -- TODO: make either `Spec_obj` or `Spec.obj` the simp-normal form. `LocallyRingedSpace_obj` is
 -- the simp-normal form of `toLocallyRingedSpace.obj`, but adding `simps` here without `attrs := []`
 -- for the same effect caused problems in mathlib4.
 /-- The spectrum, as a contravariant functor from commutative rings to schemes.
 -/
 @[simps (config := { attrs := [] })]
-def spec : CommRingCatᵒᵖ ⥤ Scheme where
+def Spec : CommRingCatᵒᵖ ⥤ Scheme where
   obj R := specObj (unop R)
   map R S f := specMap f.unop
   map_id' R := by rw [unop_id, Spec_map_id]
   map_comp' R S T f g := by rw [unop_comp, Spec_map_comp]
-#align algebraic_geometry.Scheme.Spec AlgebraicGeometry.Scheme.spec
+#align algebraic_geometry.Scheme.Spec AlgebraicGeometry.Scheme.Spec
+-/
 
+#print AlgebraicGeometry.Scheme.empty /-
 /-- The empty scheme.
 -/
 @[simps]
@@ -220,6 +267,7 @@ def empty.{u} : Scheme.{u} where
   LocalRing x := PEmpty.elim x
   local_affine x := PEmpty.elim x
 #align algebraic_geometry.Scheme.empty AlgebraicGeometry.Scheme.empty
+-/
 
 instance : EmptyCollection Scheme :=
   ⟨empty⟩
@@ -227,71 +275,96 @@ instance : EmptyCollection Scheme :=
 instance : Inhabited Scheme :=
   ⟨∅⟩
 
+#print AlgebraicGeometry.Scheme.Γ /-
 /-- The global sections, notated Gamma.
 -/
 def Γ : Schemeᵒᵖ ⥤ CommRingCat :=
   (inducedFunctor Scheme.toLocallyRingedSpace).op ⋙ LocallyRingedSpace.Γ
 #align algebraic_geometry.Scheme.Γ AlgebraicGeometry.Scheme.Γ
+-/
 
+#print AlgebraicGeometry.Scheme.Γ_def /-
 theorem Γ_def : Γ = (inducedFunctor Scheme.toLocallyRingedSpace).op ⋙ LocallyRingedSpace.Γ :=
   rfl
 #align algebraic_geometry.Scheme.Γ_def AlgebraicGeometry.Scheme.Γ_def
+-/
 
+#print AlgebraicGeometry.Scheme.Γ_obj /-
 @[simp]
 theorem Γ_obj (X : Schemeᵒᵖ) : Γ.obj X = (unop X).Presheaf.obj (op ⊤) :=
   rfl
 #align algebraic_geometry.Scheme.Γ_obj AlgebraicGeometry.Scheme.Γ_obj
+-/
 
+#print AlgebraicGeometry.Scheme.Γ_obj_op /-
 theorem Γ_obj_op (X : Scheme) : Γ.obj (op X) = X.Presheaf.obj (op ⊤) :=
   rfl
 #align algebraic_geometry.Scheme.Γ_obj_op AlgebraicGeometry.Scheme.Γ_obj_op
+-/
 
+#print AlgebraicGeometry.Scheme.Γ_map /-
 @[simp]
 theorem Γ_map {X Y : Schemeᵒᵖ} (f : X ⟶ Y) : Γ.map f = f.unop.1.c.app (op ⊤) :=
   rfl
 #align algebraic_geometry.Scheme.Γ_map AlgebraicGeometry.Scheme.Γ_map
+-/
 
+#print AlgebraicGeometry.Scheme.Γ_map_op /-
 theorem Γ_map_op {X Y : Scheme} (f : X ⟶ Y) : Γ.map f.op = f.1.c.app (op ⊤) :=
   rfl
 #align algebraic_geometry.Scheme.Γ_map_op AlgebraicGeometry.Scheme.Γ_map_op
+-/
 
 section BasicOpen
 
 variable (X : Scheme) {V U : Opens X.carrier} (f g : X.Presheaf.obj (op U))
 
+#print AlgebraicGeometry.Scheme.basicOpen /-
 /-- The subset of the underlying space where the given section does not vanish. -/
 def basicOpen : Opens X.carrier :=
   X.toLocallyRingedSpace.toRingedSpace.basicOpen f
 #align algebraic_geometry.Scheme.basic_open AlgebraicGeometry.Scheme.basicOpen
+-/
 
+#print AlgebraicGeometry.Scheme.mem_basicOpen /-
 @[simp]
 theorem mem_basicOpen (x : U) : ↑x ∈ X.basicOpen f ↔ IsUnit (X.Presheaf.germ x f) :=
   RingedSpace.mem_basicOpen _ _ _
 #align algebraic_geometry.Scheme.mem_basic_open AlgebraicGeometry.Scheme.mem_basicOpen
+-/
 
+#print AlgebraicGeometry.Scheme.mem_basicOpen_top /-
 @[simp]
 theorem mem_basicOpen_top (f : X.Presheaf.obj (op ⊤)) (x : X.carrier) :
     x ∈ X.basicOpen f ↔ IsUnit (X.Presheaf.germ (⟨x, trivial⟩ : (⊤ : Opens _)) f) :=
   RingedSpace.mem_basicOpen _ f ⟨x, trivial⟩
 #align algebraic_geometry.Scheme.mem_basic_open_top AlgebraicGeometry.Scheme.mem_basicOpen_top
+-/
 
+#print AlgebraicGeometry.Scheme.basicOpen_res /-
 @[simp]
 theorem basicOpen_res (i : op U ⟶ op V) : X.basicOpen (X.Presheaf.map i f) = V ⊓ X.basicOpen f :=
   RingedSpace.basicOpen_res _ i f
 #align algebraic_geometry.Scheme.basic_open_res AlgebraicGeometry.Scheme.basicOpen_res
+-/
 
+#print AlgebraicGeometry.Scheme.basicOpen_res_eq /-
 -- This should fire before `basic_open_res`.
 @[simp]
 theorem basicOpen_res_eq (i : op U ⟶ op V) [IsIso i] :
     X.basicOpen (X.Presheaf.map i f) = X.basicOpen f :=
   RingedSpace.basicOpen_res_eq _ i f
 #align algebraic_geometry.Scheme.basic_open_res_eq AlgebraicGeometry.Scheme.basicOpen_res_eq
+-/
 
+#print AlgebraicGeometry.Scheme.basicOpen_le /-
 @[sheaf_restrict]
 theorem basicOpen_le : X.basicOpen f ≤ U :=
   RingedSpace.basicOpen_le _ _
 #align algebraic_geometry.Scheme.basic_open_le AlgebraicGeometry.Scheme.basicOpen_le
+-/
 
+#print AlgebraicGeometry.Scheme.preimage_basicOpen /-
 @[simp]
 theorem preimage_basicOpen {X Y : Scheme} (f : X ⟶ Y) {U : Opens Y.carrier}
     (r : Y.Presheaf.obj <| op U) :
@@ -299,27 +372,35 @@ theorem preimage_basicOpen {X Y : Scheme} (f : X ⟶ Y) {U : Opens Y.carrier}
       @Scheme.basicOpen X ((Opens.map f.1.base).obj U) (f.1.c.app _ r) :=
   LocallyRingedSpace.preimage_basicOpen f r
 #align algebraic_geometry.Scheme.preimage_basic_open AlgebraicGeometry.Scheme.preimage_basicOpen
+-/
 
+#print AlgebraicGeometry.Scheme.basicOpen_zero /-
 @[simp]
 theorem basicOpen_zero (U : Opens X.carrier) : X.basicOpen (0 : X.Presheaf.obj <| op U) = ⊥ :=
   LocallyRingedSpace.basicOpen_zero _ U
 #align algebraic_geometry.Scheme.basic_open_zero AlgebraicGeometry.Scheme.basicOpen_zero
+-/
 
+#print AlgebraicGeometry.Scheme.basicOpen_mul /-
 @[simp]
 theorem basicOpen_mul : X.basicOpen (f * g) = X.basicOpen f ⊓ X.basicOpen g :=
   RingedSpace.basicOpen_mul _ _ _
 #align algebraic_geometry.Scheme.basic_open_mul AlgebraicGeometry.Scheme.basicOpen_mul
+-/
 
+#print AlgebraicGeometry.Scheme.basicOpen_of_isUnit /-
 theorem basicOpen_of_isUnit {f : X.Presheaf.obj (op U)} (hf : IsUnit f) : X.basicOpen f = U :=
   RingedSpace.basicOpen_of_isUnit _ hf
 #align algebraic_geometry.Scheme.basic_open_of_is_unit AlgebraicGeometry.Scheme.basicOpen_of_isUnit
+-/
 
 end BasicOpen
 
 end Scheme
 
+#print AlgebraicGeometry.basicOpen_eq_of_affine /-
 theorem basicOpen_eq_of_affine {R : CommRingCat} (f : R) :
-    (Scheme.spec.obj <| op R).basicOpen ((SpecΓIdentity.app R).inv f) = PrimeSpectrum.basicOpen f :=
+    (Scheme.Spec.obj <| op R).basicOpen ((SpecΓIdentity.app R).inv f) = PrimeSpectrum.basicOpen f :=
   by
   ext
   erw [Scheme.mem_basic_open_top]
@@ -331,15 +412,18 @@ theorem basicOpen_eq_of_affine {R : CommRingCat} (f : R) :
         (PrimeSpectrum.asIdeal x) f :
       _)
 #align algebraic_geometry.basic_open_eq_of_affine AlgebraicGeometry.basicOpen_eq_of_affine
+-/
 
+#print AlgebraicGeometry.basicOpen_eq_of_affine' /-
 @[simp]
 theorem basicOpen_eq_of_affine' {R : CommRingCat}
     (f : (Spec.toSheafedSpace.obj (op R)).Presheaf.obj (op ⊤)) :
-    (Scheme.spec.obj <| op R).basicOpen f = PrimeSpectrum.basicOpen ((SpecΓIdentity.app R).Hom f) :=
+    (Scheme.Spec.obj <| op R).basicOpen f = PrimeSpectrum.basicOpen ((SpecΓIdentity.app R).Hom f) :=
   by
   convert basic_open_eq_of_affine ((Spec_Γ_identity.app R).Hom f)
   exact (iso.hom_inv_id_apply _ _).symm
 #align algebraic_geometry.basic_open_eq_of_affine' AlgebraicGeometry.basicOpen_eq_of_affine'
+-/
 
 end AlgebraicGeometry

88474d1b

bump to nightly-2023-06-16-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/bf9bbbcf0c1c1ead18280b0d010e417b10abb1b6

39cf1563

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebraic_geometry.Scheme
-! leanprover-community/mathlib commit 06c75afebd8b612d3b20fe836424298f2387ca53
+! leanprover-community/mathlib commit 88474d1b5af6d37c2ab728b757771bced7f5194c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.Category.Ring.Constructions
 /-!
 # The category of schemes
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A scheme is a locally ringed space such that every point is contained in some open set
 where there is an isomorphism of presheaves between the restriction to that open set,
 and the structure sheaf of `Spec R`, for some commutative ring `R`.
@@ -194,9 +197,12 @@ theorem specMap_comp {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T) :
   Spec.locallyRingedSpaceMap_comp f g
 #align algebraic_geometry.Scheme.Spec_map_comp AlgebraicGeometry.Scheme.specMap_comp
 
+-- TODO: make either `Spec_obj` or `Spec.obj` the simp-normal form. `LocallyRingedSpace_obj` is
+-- the simp-normal form of `toLocallyRingedSpace.obj`, but adding `simps` here without `attrs := []`
+-- for the same effect caused problems in mathlib4.
 /-- The spectrum, as a contravariant functor from commutative rings to schemes.
 -/
-@[simps]
+@[simps (config := { attrs := [] })]
 def spec : CommRingCatᵒᵖ ⥤ Scheme where
   obj R := specObj (unop R)
   map R S f := specMap f.unop

06c75afe

bump to nightly-2023-06-14-05

mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8

6c112b6f

Diff

@@ -313,7 +313,7 @@ end BasicOpen
 end Scheme
 
 theorem basicOpen_eq_of_affine {R : CommRingCat} (f : R) :
-    (Scheme.spec.obj <| op R).basicOpen ((specΓIdentity.app R).inv f) = PrimeSpectrum.basicOpen f :=
+    (Scheme.spec.obj <| op R).basicOpen ((SpecΓIdentity.app R).inv f) = PrimeSpectrum.basicOpen f :=
   by
   ext
   erw [Scheme.mem_basic_open_top]
@@ -329,7 +329,7 @@ theorem basicOpen_eq_of_affine {R : CommRingCat} (f : R) :
 @[simp]
 theorem basicOpen_eq_of_affine' {R : CommRingCat}
     (f : (Spec.toSheafedSpace.obj (op R)).Presheaf.obj (op ⊤)) :
-    (Scheme.spec.obj <| op R).basicOpen f = PrimeSpectrum.basicOpen ((specΓIdentity.app R).Hom f) :=
+    (Scheme.spec.obj <| op R).basicOpen f = PrimeSpectrum.basicOpen ((SpecΓIdentity.app R).Hom f) :=
   by
   convert basic_open_eq_of_affine ((Spec_Γ_identity.app R).Hom f)
   exact (iso.hom_inv_id_apply _ _).symm

06c75afe

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -35,7 +35,7 @@ open Opposite
 
 namespace AlgebraicGeometry
 
-/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
 /-- We define `Scheme` as a `X : LocallyRingedSpace`,
 along with a proof that every point has an open neighbourhood `U`
 so that that the restriction of `X` to `U` is isomorphic,
@@ -43,7 +43,7 @@ as a locally ringed space, to `Spec.to_LocallyRingedSpace.obj (op R)`
 for some `R : CommRing`.
 -/
 structure Scheme extends
-    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure" where
+    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure" where
   local_affine :
     ∀ x : to_LocallyRingedSpace,
       ∃ (U : OpenNhds x) (R : CommRingCat),

06c75afe

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -35,7 +35,7 @@ open Opposite
 
 namespace AlgebraicGeometry
 
-/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
 /-- We define `Scheme` as a `X : LocallyRingedSpace`,
 along with a proof that every point has an open neighbourhood `U`
 so that that the restriction of `X` to `U` is isomorphic,
@@ -43,7 +43,7 @@ as a locally ringed space, to `Spec.to_LocallyRingedSpace.obj (op R)`
 for some `R : CommRing`.
 -/
 structure Scheme extends
-    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure" where
+    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure" where
   local_affine :
     ∀ x : to_LocallyRingedSpace,
       ∃ (U : OpenNhds x) (R : CommRingCat),

06c75afe

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -43,10 +43,10 @@ as a locally ringed space, to `Spec.to_LocallyRingedSpace.obj (op R)`
 for some `R : CommRing`.
 -/
 structure Scheme extends
-  "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure" where
+    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure" where
   local_affine :
     ∀ x : to_LocallyRingedSpace,
-      ∃ (U : OpenNhds x)(R : CommRingCat),
+      ∃ (U : OpenNhds x) (R : CommRingCat),
         Nonempty
           (to_LocallyRingedSpace.restrict U.OpenEmbedding ≅ Spec.toLocallyRingedSpace.obj (op R))
 #align algebraic_geometry.Scheme AlgebraicGeometry.Scheme
@@ -73,7 +73,8 @@ protected abbrev sheaf (X : Scheme) :=
 /-- The forgetful functor from `Scheme` to `LocallyRingedSpace`. -/
 @[simps]
 def forgetToLocallyRingedSpace : Scheme ⥤ LocallyRingedSpace :=
-  inducedFunctor _ deriving Full, Faithful
+  inducedFunctor _
+deriving Full, Faithful
 #align algebraic_geometry.Scheme.forget_to_LocallyRingedSpace AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
 
 @[simp]

06c75afe

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -96,12 +96,7 @@ theorem id_val_base (X : Scheme) : (𝟙 X : _).1.base = 𝟙 _ :=
 @[simp]
 theorem id_app {X : Scheme} (U : (Opens X.carrier)ᵒᵖ) :
     (𝟙 X : _).val.c.app U =
-      X.Presheaf.map
-        (eqToHom
-          (by
-            induction U using Opposite.rec'
-            cases U
-            rfl)) :=
+      X.Presheaf.map (eqToHom (by induction U using Opposite.rec'; cases U; rfl)) :=
   PresheafedSpace.id_c_app X.toPresheafedSpace U
 #align algebraic_geometry.Scheme.id_app AlgebraicGeometry.Scheme.id_app
 
@@ -129,11 +124,7 @@ theorem comp_val_c_app {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
 #align algebraic_geometry.Scheme.comp_val_c_app AlgebraicGeometry.Scheme.comp_val_c_app
 
 theorem congr_app {X Y : Scheme} {f g : X ⟶ Y} (e : f = g) (U) :
-    f.val.c.app U = g.val.c.app U ≫ X.Presheaf.map (eqToHom (by subst e)) :=
-  by
-  subst e
-  dsimp
-  simp
+    f.val.c.app U = g.val.c.app U ≫ X.Presheaf.map (eqToHom (by subst e)) := by subst e; dsimp; simp
 #align algebraic_geometry.Scheme.congr_app AlgebraicGeometry.Scheme.congr_app
 
 theorem app_eq {X Y : Scheme} (f : X ⟶ Y) {U V : Opens Y.carrier} (e : U = V) :
@@ -154,10 +145,7 @@ instance is_locallyRingedSpace_iso {X Y : Scheme} (f : X ⟶ Y) [IsIso f] :
 theorem inv_val_c_app {X Y : Scheme} (f : X ⟶ Y) [IsIso f] (U : Opens X.carrier) :
     (inv f).val.c.app (op U) =
       X.Presheaf.map
-          (eqToHom <| by
-                rw [is_iso.hom_inv_id]
-                ext1
-                rfl :
+          (eqToHom <| by rw [is_iso.hom_inv_id]; ext1; rfl :
               (Opens.map (f ≫ inv f).1.base).obj U ⟶ U).op ≫
         inv (f.val.c.app (op <| (Opens.map _).obj U)) :=
   by

06c75afe

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -105,24 +105,24 @@ theorem id_app {X : Scheme} (U : (Opens X.carrier)ᵒᵖ) :
   PresheafedSpace.id_c_app X.toPresheafedSpace U
 #align algebraic_geometry.Scheme.id_app AlgebraicGeometry.Scheme.id_app
 
-@[reassoc.1]
+@[reassoc]
 theorem comp_val {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) : (f ≫ g).val = f.val ≫ g.val :=
   rfl
 #align algebraic_geometry.Scheme.comp_val AlgebraicGeometry.Scheme.comp_val
 
-@[reassoc.1, simp]
+@[reassoc, simp]
 theorem comp_coeBase {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).val.base = f.val.base ≫ g.val.base :=
   rfl
 #align algebraic_geometry.Scheme.comp_coe_base AlgebraicGeometry.Scheme.comp_coeBase
 
-@[reassoc.1, elementwise]
+@[reassoc, elementwise]
 theorem comp_val_base {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).val.base = f.val.base ≫ g.val.base :=
   rfl
 #align algebraic_geometry.Scheme.comp_val_base AlgebraicGeometry.Scheme.comp_val_base
 
-@[reassoc.1, simp]
+@[reassoc, simp]
 theorem comp_val_c_app {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (f ≫ g).val.c.app U = g.val.c.app U ≫ f.val.c.app _ :=
   rfl

06c75afe

bump to nightly-2023-04-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

ff662d55

Diff

@@ -35,7 +35,7 @@ open Opposite
 
 namespace AlgebraicGeometry
 
-/- ./././Mathport/Syntax/Translate/Command.lean:417:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
 /-- We define `Scheme` as a `X : LocallyRingedSpace`,
 along with a proof that every point has an open neighbourhood `U`
 so that that the restriction of `X` to `U` is isomorphic,
@@ -43,7 +43,7 @@ as a locally ringed space, to `Spec.to_LocallyRingedSpace.obj (op R)`
 for some `R : CommRing`.
 -/
 structure Scheme extends
-  "./././Mathport/Syntax/Translate/Command.lean:417:11: unsupported: advanced extends in structure" where
+  "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure" where
   local_affine :
     ∀ x : to_LocallyRingedSpace,
       ∃ (U : OpenNhds x)(R : CommRingCat),

06c75afe

bump to nightly-2023-04-18-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

c37d1701

Diff

@@ -99,7 +99,7 @@ theorem id_app {X : Scheme} (U : (Opens X.carrier)ᵒᵖ) :
       X.Presheaf.map
         (eqToHom
           (by
-            induction U using Opposite.rec
+            induction U using Opposite.rec'
             cases U
             rfl)) :=
   PresheafedSpace.id_c_app X.toPresheafedSpace U

06c75afe

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

88474d1b

chore(CategoryTheory): make Functor.Full a Prop (#12449)

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

ce289a0e

Diff

@@ -87,7 +87,7 @@ instance : forgetToLocallyRingedSpace.Faithful :=
 @[simp]
 theorem forgetToLocallyRingedSpace_preimage {X Y : Scheme} (f : X ⟶ Y) :
     Scheme.forgetToLocallyRingedSpace.preimage f = f :=
-  rfl
+  Scheme.forgetToLocallyRingedSpace.map_injective (Functor.map_preimage _ _)
 #align algebraic_geometry.Scheme.forget_to_LocallyRingedSpace_preimage AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace_preimage
 
 /-- The forgetful functor from `Scheme` to `TopCat`. -/

88474d1b

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -49,7 +49,7 @@ structure Scheme extends LocallyRingedSpace where
 namespace Scheme
 
 /-- A morphism between schemes is a morphism between the underlying locally ringed spaces. -/
--- @[nolint has_nonempty_instance] -- Porting note: no such linter.
+-- @[nolint has_nonempty_instance] -- Porting note(#5171): linter not ported yet
 def Hom (X Y : Scheme) : Type* :=
   X.toLocallyRingedSpace ⟶ Y.toLocallyRingedSpace
 #align algebraic_geometry.Scheme.hom AlgebraicGeometry.Scheme.Hom

88474d1b

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

65b7affc

Diff

@@ -78,10 +78,10 @@ def forgetToLocallyRingedSpace : Scheme ⥤ LocallyRingedSpace :=
 -- deriving Full, Faithful -- Porting note: no delta derive handler, see https://github.com/leanprover-community/mathlib4/issues/5020
 #align algebraic_geometry.Scheme.forget_to_LocallyRingedSpace AlgebraicGeometry.Scheme.forgetToLocallyRingedSpace
 
-instance : Full forgetToLocallyRingedSpace :=
+instance : forgetToLocallyRingedSpace.Full :=
   InducedCategory.full _
 
-instance : Faithful forgetToLocallyRingedSpace :=
+instance : forgetToLocallyRingedSpace.Faithful :=
   InducedCategory.faithful _
 
 @[simp]

88474d1b

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -231,7 +231,7 @@ theorem specMap_comp {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T) :
 
 /-- The spectrum, as a contravariant functor from commutative rings to schemes.
 -/
--- porting note: removed @[simps]
+-- Porting note: removed @[simps]
 -- TODO: We need to decide whether `Spec_obj` or `Spec.obj` the simp-normal form.
 -- We probably want `Spec.obj`, but note
 -- `locallyRingedSpaceObj` is currently the simp-normal form of `toLocallyRingedSpace.obj`.

88474d1b

style: reduce spacing variation in "porting note" comments (#10886)

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

86b84c52

Diff

@@ -96,11 +96,11 @@ def forgetToTop : Scheme ⥤ TopCat :=
   Scheme.forgetToLocallyRingedSpace ⋙ LocallyRingedSpace.forgetToTop
 #align algebraic_geometry.Scheme.forget_to_Top AlgebraicGeometry.Scheme.forgetToTop
 
--- Porting note : Lean seems not able to find this coercion any more
+-- Porting note: Lean seems not able to find this coercion any more
 instance hasCoeToTopCat : CoeOut Scheme TopCat where
   coe X := X.carrier
 
--- Porting note : added this unification hint just in case
+-- Porting note: added this unification hint just in case
 /-- forgetful functor to `TopCat` is the same as coercion -/
 unif_hint forgetToTop_obj_eq_coe (X : Scheme) where ⊢
   forgetToTop.obj X ≟ (X : TopCat)
@@ -161,7 +161,7 @@ theorem app_eq {X Y : Scheme} (f : X ⟶ Y) {U V : Opens Y.carrier} (e : U = V)
   rfl
 #align algebraic_geometry.Scheme.app_eq AlgebraicGeometry.Scheme.app_eq
 
--- Porting note : in `AffineScheme.lean` file, `eqToHom_op` can't be used in `(e)rw` or `simp(_rw)`
+-- Porting note: in `AffineScheme.lean` file, `eqToHom_op` can't be used in `(e)rw` or `simp(_rw)`
 -- when terms get very complicated. See `AlgebraicGeometry.IsAffineOpen.isLocalization_stalk_aux`.
 lemma presheaf_map_eqToHom_op (X : Scheme) (U V : Opens X) (i : U = V) :
     X.presheaf.map (eqToHom i).op = eqToHom (i ▸ rfl) := by

88474d1b

chore: classify added to ease automation porting notes (#10689)

Classifies by adding issue number (#10688) to porting notes claiming anything semantically equivalent to added to ease automation.
Enforce singular convention converting "porting notes" to "porting note".

b06068c3

Diff

@@ -59,7 +59,7 @@ def Hom (X Y : Scheme) : Type* :=
 instance : Category Scheme :=
   { InducedCategory.category Scheme.toLocallyRingedSpace with Hom := Hom }
 
--- porting note: added to ease automation
+-- porting note (#10688): added to ease automation
 @[continuity]
 lemma Hom.continuous {X Y : Scheme} (f : X ⟶ Y) : Continuous f.1.base := f.1.base.2

88474d1b

perf(FunLike.Basic): beta reduce CoeFun.coe (#7905)

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

e194c756

Diff

@@ -342,7 +342,7 @@ lemma basicOpen_restrict (i : V ⟶ U) (f : X.presheaf.obj (op U)) :
 theorem preimage_basicOpen {X Y : Scheme} (f : X ⟶ Y) {U : Opens Y.carrier}
     (r : Y.presheaf.obj <| op U) :
     (Opens.map f.1.base).obj (Y.basicOpen r) =
-      @Scheme.basicOpen X ((Opens.map f.1.base).obj U) (f.1.c.app _ r) :=
+      @Scheme.basicOpen X ((Opens.map f.1.base).obj U) (f.1.c.app (op U) r) :=
   LocallyRingedSpace.preimage_basicOpen f r
 #align algebraic_geometry.Scheme.preimage_basic_open AlgebraicGeometry.Scheme.preimage_basicOpen

88474d1b

perf(AlgebraicGeometry): Fix slow and bad proofs (#7747)

Fixed AlgebraicGeometry/AffineSchemes.lean, AlgebraicGeometry/Morphisms/QuasiSeparated.lean and AlgebraicGeometry/Morphisms/RingHomProperties.lean.

Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Mauricio Collares <mauricio@collares.org>

ace6e091

Diff

@@ -190,6 +190,9 @@ theorem inv_val_c_app {X Y : Scheme} (f : X ⟶ Y) [IsIso f] (U : Opens X.carrie
     eqToHom_op]
 #align algebraic_geometry.Scheme.inv_val_c_app AlgebraicGeometry.Scheme.inv_val_c_app
 
+theorem inv_val_c_app_top {X Y : Scheme} (f : X ⟶ Y) [IsIso f] :
+    (inv f).val.c.app (op ⊤) = inv (f.val.c.app (op ⊤)) := by simp
+
 /-- Given a morphism of schemes `f : X ⟶ Y`, and open sets `U ⊆ Y`, `V ⊆ f ⁻¹' U`,
 this is the induced map `Γ(Y, U) ⟶ Γ(X, V)`. -/
 abbrev Hom.appLe {X Y : Scheme} (f : X ⟶ Y) {V : Opens X.carrier} {U : Opens Y.carrier}
@@ -289,6 +292,7 @@ section BasicOpen
 variable (X : Scheme) {V U : Opens X.carrier} (f g : X.presheaf.obj (op U))
 
 /-- The subset of the underlying space where the given section does not vanish. -/
+@[pp_dot]
 def basicOpen : Opens X.carrier :=
   X.toLocallyRingedSpace.toRingedSpace.basicOpen f
 #align algebraic_geometry.Scheme.basic_open AlgebraicGeometry.Scheme.basicOpen
@@ -298,7 +302,6 @@ theorem mem_basicOpen (x : U) : ↑x ∈ X.basicOpen f ↔ IsUnit (X.presheaf.ge
   RingedSpace.mem_basicOpen _ _ _
 #align algebraic_geometry.Scheme.mem_basic_open AlgebraicGeometry.Scheme.mem_basicOpen
 
-@[aesop norm simp (rule_sets [Restrict])]
 theorem mem_basicOpen_top' {U : Opens X} (f : X.presheaf.obj (op U)) (x : X.carrier) :
     x ∈ X.basicOpen f ↔ ∃ (m : x ∈ U), IsUnit (X.presheaf.germ (⟨x, m⟩ : U) f) := by
   fconstructor
@@ -330,6 +333,11 @@ theorem basicOpen_le : X.basicOpen f ≤ U :=
   RingedSpace.basicOpen_le _ _
 #align algebraic_geometry.Scheme.basic_open_le AlgebraicGeometry.Scheme.basicOpen_le
 
+@[sheaf_restrict]
+lemma basicOpen_restrict (i : V ⟶ U) (f : X.presheaf.obj (op U)) :
+    X.basicOpen (f |_ₕ i) ≤ X.basicOpen f :=
+  (Scheme.basicOpen_res _ _ _).trans_le inf_le_right
+
 @[simp]
 theorem preimage_basicOpen {X Y : Scheme} (f : X ⟶ Y) {U : Opens Y.carrier}
     (r : Y.presheaf.obj <| op U) :
@@ -352,6 +360,10 @@ theorem basicOpen_of_isUnit {f : X.presheaf.obj (op U)} (hf : IsUnit f) : X.basi
   RingedSpace.basicOpen_of_isUnit _ hf
 #align algebraic_geometry.Scheme.basic_open_of_is_unit AlgebraicGeometry.Scheme.basicOpen_of_isUnit
 
+instance algebra_section_section_basicOpen {X : Scheme} {U : Opens X} (f : X.presheaf.obj (op U)) :
+    Algebra (X.presheaf.obj (op U)) (X.presheaf.obj (op <| X.basicOpen f)) :=
+  (X.presheaf.map (homOfLE <| X.basicOpen_le f : _ ⟶ U).op).toAlgebra
+
 end BasicOpen
 
 end Scheme
@@ -379,4 +391,14 @@ theorem basicOpen_eq_of_affine' {R : CommRingCat}
   exact (Iso.hom_inv_id_apply (SpecΓIdentity.app R) f).symm
 #align algebraic_geometry.basic_open_eq_of_affine' AlgebraicGeometry.basicOpen_eq_of_affine'
 
+theorem Scheme.Spec_map_presheaf_map_eqToHom {X : Scheme} {U V : Opens X} (h : U = V) (W) :
+    (Scheme.Spec.map (X.presheaf.map (eqToHom h).op).op).val.c.app W =
+      eqToHom (by cases h; induction W using Opposite.rec'; dsimp; simp) := by
+  have : Scheme.Spec.map (X.presheaf.map (𝟙 (op U))).op = 𝟙 _ := by
+    rw [X.presheaf.map_id, op_id, Scheme.Spec.map_id]
+  cases h
+  refine' (Scheme.congr_app this _).trans _
+  simp [eqToHom_map]
+#align algebraic_geometry.Scheme.Spec_map_presheaf_map_eqToHom AlgebraicGeometry.Scheme.Spec_map_presheaf_map_eqToHom
+
 end AlgebraicGeometry

88474d1b

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -50,7 +50,7 @@ namespace Scheme
 
 /-- A morphism between schemes is a morphism between the underlying locally ringed spaces. -/
 -- @[nolint has_nonempty_instance] -- Porting note: no such linter.
-def Hom (X Y : Scheme) : Type _ :=
+def Hom (X Y : Scheme) : Type* :=
   X.toLocallyRingedSpace ⟶ Y.toLocallyRingedSpace
 #align algebraic_geometry.Scheme.hom AlgebraicGeometry.Scheme.Hom
 
@@ -68,7 +68,7 @@ protected abbrev sheaf (X : Scheme) :=
   X.toSheafedSpace.sheaf
 #align algebraic_geometry.Scheme.sheaf AlgebraicGeometry.Scheme.sheaf
 
-instance : CoeSort Scheme (Type _) where
+instance : CoeSort Scheme (Type*) where
   coe X := X.carrier
 
 /-- The forgetful functor from `Scheme` to `LocallyRingedSpace`. -/

88474d1b

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebraic_geometry.Scheme
-! leanprover-community/mathlib commit 88474d1b5af6d37c2ab728b757771bced7f5194c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicGeometry.Spec
 import Mathlib.Algebra.Category.Ring.Constructions
 
+#align_import algebraic_geometry.Scheme from "leanprover-community/mathlib"@"88474d1b5af6d37c2ab728b757771bced7f5194c"
+
 /-!
 # The category of schemes

88474d1b

chore: forward port #19188 (#5709)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

d3e6efa7

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebraic_geometry.Scheme
-! leanprover-community/mathlib commit 06c75afebd8b612d3b20fe836424298f2387ca53
+! leanprover-community/mathlib commit 88474d1b5af6d37c2ab728b757771bced7f5194c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -232,6 +232,9 @@ theorem specMap_comp {R S T : CommRingCat} (f : R ⟶ S) (g : S ⟶ T) :
 /-- The spectrum, as a contravariant functor from commutative rings to schemes.
 -/
 -- porting note: removed @[simps]
+-- TODO: We need to decide whether `Spec_obj` or `Spec.obj` the simp-normal form.
+-- We probably want `Spec.obj`, but note
+-- `locallyRingedSpaceObj` is currently the simp-normal form of `toLocallyRingedSpace.obj`.
 def Spec : CommRingCatᵒᵖ ⥤ Scheme where
   obj R := specObj (unop R)
   map f := specMap f.unop

06c75afe

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -302,9 +302,9 @@ theorem mem_basicOpen (x : U) : ↑x ∈ X.basicOpen f ↔ IsUnit (X.presheaf.ge
 theorem mem_basicOpen_top' {U : Opens X} (f : X.presheaf.obj (op U)) (x : X.carrier) :
     x ∈ X.basicOpen f ↔ ∃ (m : x ∈ U), IsUnit (X.presheaf.germ (⟨x, m⟩ : U) f) := by
   fconstructor
-  . rintro ⟨y, hy1, rfl⟩
+  · rintro ⟨y, hy1, rfl⟩
     exact ⟨y.2, hy1⟩
-  . rintro ⟨m, hm⟩
+  · rintro ⟨m, hm⟩
     exact ⟨⟨x, m⟩, hm, rfl⟩
 
 @[simp]

06c75afe

feat: port AlgebraicGeometry.Morphisms.QuasiCompact (#5642)

Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com>

c156373e

Diff

@@ -62,6 +62,10 @@ def Hom (X Y : Scheme) : Type _ :=
 instance : Category Scheme :=
   { InducedCategory.category Scheme.toLocallyRingedSpace with Hom := Hom }
 
+-- porting note: added to ease automation
+@[continuity]
+lemma Hom.continuous {X Y : Scheme} (f : X ⟶ Y) : Continuous f.1.base := f.1.base.2
+
 /-- The structure sheaf of a scheme. -/
 protected abbrev sheaf (X : Scheme) :=
   X.toSheafedSpace.sheaf
@@ -294,6 +298,15 @@ theorem mem_basicOpen (x : U) : ↑x ∈ X.basicOpen f ↔ IsUnit (X.presheaf.ge
   RingedSpace.mem_basicOpen _ _ _
 #align algebraic_geometry.Scheme.mem_basic_open AlgebraicGeometry.Scheme.mem_basicOpen
 
+@[aesop norm simp (rule_sets [Restrict])]
+theorem mem_basicOpen_top' {U : Opens X} (f : X.presheaf.obj (op U)) (x : X.carrier) :
+    x ∈ X.basicOpen f ↔ ∃ (m : x ∈ U), IsUnit (X.presheaf.germ (⟨x, m⟩ : U) f) := by
+  fconstructor
+  . rintro ⟨y, hy1, rfl⟩
+    exact ⟨y.2, hy1⟩
+  . rintro ⟨m, hm⟩
+    exact ⟨⟨x, m⟩, hm, rfl⟩
+
 @[simp]
 theorem mem_basicOpen_top (f : X.presheaf.obj (op ⊤)) (x : X.carrier) :
     x ∈ X.basicOpen f ↔ IsUnit (X.presheaf.germ (⟨x, trivial⟩ : (⊤ : Opens _)) f) :=

06c75afe

chore: fix grammar in docs (#5668)

15cdb8ec

Diff

@@ -35,7 +35,7 @@ open Opposite
 
 namespace AlgebraicGeometry
 
-/-- We define `Scheme` as a `X : LocallyRingedSpace`,
+/-- We define `Scheme` as an `X : LocallyRingedSpace`,
 along with a proof that every point has an open neighbourhood `U`
 so that that the restriction of `X` to `U` is isomorphic,
 as a locally ringed space, to `Spec.toLocallyRingedSpace.obj (op R)`

06c75afe

feat: port AlgebraicGeometry.FunctionField (#5596)

Co-authored-by: yuma-mizuno <mizuno.y.aj@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

e3884c33

Diff

@@ -134,6 +134,11 @@ theorem comp_val_base {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) :
   rfl
 #align algebraic_geometry.Scheme.comp_val_base AlgebraicGeometry.Scheme.comp_val_base
 
+theorem comp_val_base_apply {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (x : X) :
+    (f ≫ g).val.base x = g.val.base (f.val.base x) := by
+  simp
+#align algebraic_geometry.Scheme.comp_val_base_apply AlgebraicGeometry.Scheme.comp_val_base_apply
+
 @[simp, reassoc] -- reassoc lemma does not need `simp`
 theorem comp_val_c_app {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (U) :
     (f ≫ g).val.c.app U = g.val.c.app U ≫ f.val.c.app _ :=

06c75afe

feat: port AlgebraicGeometry.AffineScheme (#5394)

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

a5ab9709

Diff

@@ -95,6 +95,15 @@ def forgetToTop : Scheme ⥤ TopCat :=
   Scheme.forgetToLocallyRingedSpace ⋙ LocallyRingedSpace.forgetToTop
 #align algebraic_geometry.Scheme.forget_to_Top AlgebraicGeometry.Scheme.forgetToTop
 
+-- Porting note : Lean seems not able to find this coercion any more
+instance hasCoeToTopCat : CoeOut Scheme TopCat where
+  coe X := X.carrier
+
+-- Porting note : added this unification hint just in case
+/-- forgetful functor to `TopCat` is the same as coercion -/
+unif_hint forgetToTop_obj_eq_coe (X : Scheme) where ⊢
+  forgetToTop.obj X ≟ (X : TopCat)
+
 @[simp]
 theorem id_val_base (X : Scheme) : (𝟙 X : _).1.base = 𝟙 _ :=
   rfl
@@ -146,6 +155,12 @@ theorem app_eq {X Y : Scheme} (f : X ⟶ Y) {U V : Opens Y.carrier} (e : U = V)
   rfl
 #align algebraic_geometry.Scheme.app_eq AlgebraicGeometry.Scheme.app_eq
 
+-- Porting note : in `AffineScheme.lean` file, `eqToHom_op` can't be used in `(e)rw` or `simp(_rw)`
+-- when terms get very complicated. See `AlgebraicGeometry.IsAffineOpen.isLocalization_stalk_aux`.
+lemma presheaf_map_eqToHom_op (X : Scheme) (U V : Opens X) (i : U = V) :
+    X.presheaf.map (eqToHom i).op = eqToHom (i ▸ rfl) := by
+  rw [eqToHom_op, eqToHom_map]
+
 instance is_locallyRingedSpace_iso {X Y : Scheme} (f : X ⟶ Y) [IsIso f] :
     @IsIso LocallyRingedSpace _ _ _ f :=
   forgetToLocallyRingedSpace.map_isIso f

06c75afe

feat: port AlgebraicGeometry.OpenImmersion.Scheme (#5290)

a5e9328b

Diff

@@ -67,6 +67,9 @@ protected abbrev sheaf (X : Scheme) :=
   X.toSheafedSpace.sheaf
 #align algebraic_geometry.Scheme.sheaf AlgebraicGeometry.Scheme.sheaf
 
+instance : CoeSort Scheme (Type _) where
+  coe X := X.carrier
+
 /-- The forgetful functor from `Scheme` to `LocallyRingedSpace`. -/
 @[simps!]
 def forgetToLocallyRingedSpace : Scheme ⥤ LocallyRingedSpace :=

06c75afe

feat: port AlgebraicGeometry.Scheme (#5040)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Johan Commelin <johan@commelin.net>

1a0f4dea

`algebraic_geometry.Scheme` ⟷ `Mathlib.AlgebraicGeometry.Scheme`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 904

algebraic_geometry.Scheme ⟷ Mathlib.AlgebraicGeometry.Scheme

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 904

`algebraic_geometry.Scheme` ⟷ `Mathlib.AlgebraicGeometry.Scheme`