Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.fromNormalization_app

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.QuasiCompact f]
  [inst_1 : AlgebraicGeometry.QuasiSeparated f] {U : Y.Opens} (hU : AlgebraicGeometry.IsAffineOpen U),
  AlgebraicGeometry.Scheme.Hom.app (AlgebraicGeometry.Scheme.Hom.fromNormalization f) U =
    CategoryTheory.CategoryStruct.comp
      (CommRingCat.ofHom
        (algebraMap ↑(Y.presheaf.1 (Opposite.op U))
          ↥(integralClosure ↑(Y.presheaf.obj (Opposite.op U))
              ↑(X.presheaf.obj (Opposite.op ((TopologicalSpace.Opens.map f.base).obj U))))))
      (AlgebraicGeometry.Scheme.Hom.normalizationObjIso f hU).inv

Defined in: Mathlib.AlgebraicGeometry.Normalization
Cited by: 1 results in Mathlib
Foundations: Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.QuasiCompact AlgebraicGeometry.QuasiSeparated

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Cites77

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Algebraproof · cited by 11,388
Top.topproof · cited by 9,680
CategoryTheory.Functor.mapproof · cited by 8,698
Oppositestatement · cited by 8,081
CategoryTheory.NatTrans.appproof · cited by 7,406
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
Algebra.algebraMapstatement and proof · cited by 4,706
TopCat.carrierstatement · cited by 3,184

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assocproof · cited by 0