Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.LocallyOfFiniteType f]
  [inst : AlgebraicGeometry.IsSeparated f] [inst_1 : AlgebraicGeometry.QuasiCompact f] (x : ↥X),
  AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt f x →
    ∃ V,
      (AlgebraicGeometry.Scheme.Hom.toNormalization f) x ∈ V ∧
        CategoryTheory.IsIso (AlgebraicGeometry.Scheme.Hom.toNormalization f ∣_ V)

Defined in: Mathlib.AlgebraicGeometry.ZariskisMainTheorem
Cited by: 1 results in Mathlib
Foundations: Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.LocallyOfFiniteType AlgebraicGeometry.IsSeparated AlgebraicGeometry.QuasiCompact

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

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CategoryTheory.CategoryStruct.compproof · cited by 17,999
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CategoryTheory.Iso.homproof · cited by 7,684
CategoryTheory.Iso.invproof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
Set.imageproof · cited by 5,609
Set.preimageproof · cited by 4,946

Cited by1

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AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalizationproof · cited by 1