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Mathlib/AlgebraicGeometry/Modules Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -121,12 +121,12 @@ lemma isSMulRegular_of_le_basicOpen {f : R} (hle : U ≤ PrimeSpectrum.basicOpen
121121
122122set_option backward.isDefEq.respectTransparency false in
123123@[simp]
124- lemma Scheme.Modules. restrictAppIso_smul_Spec {S : CommRingCat.{u}} (f : R ⟶ S)
124+ lemma restrictAppIso_smul_Spec {S : CommRingCat.{u}} (f : R ⟶ S)
125125 [IsOpenImmersion (Spec.map f)] {U : (Spec S).Opens} (r : R)
126126 (x : Γ(M.restrict (Spec.map f), U)) :
127127 dsimp% (M.restrictAppIso (Spec.map f) U).hom (f r • x) =
128128 r • (M.restrictAppIso (Spec.map f) U).hom x := by
129- rw [Scheme.Modules. smul_Spec_def, Scheme.Modules. smul_Spec_def]
129+ rw [smul_Spec_def, smul_Spec_def]
130130 simp_rw [smul_restrictAppIso_hom_apply, ← ConcreteCategory.comp_apply, Category.assoc]
131131 have :
132132 f ≫ (ΓSpecIso S).inv ≫ (Spec S).presheaf.map U.leTop.op ≫ (Hom.appIso (Spec.map f) U).inv =
@@ -135,6 +135,10 @@ lemma Scheme.Modules.restrictAppIso_smul_Spec {S : CommRingCat.{u}} (f : R ⟶ S
135135 rfl
136136 rw [this]
137137
138+ set_option linter.dupNamespace false in
139+ @ [deprecated (since := "2026-06-04" )]
140+ alias Scheme.Modules.restrictAppIso_smul_Spec := restrictAppIso_smul_Spec
141+
138142end Scheme.Modules
139143
140144/--
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