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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.normalizationOpenCover

{X Y : AlgebraicGeometry.Scheme} →
  (f : X ⟶ Y) →
    [inst : AlgebraicGeometry.QuasiCompact f] →
      [inst_1 : AlgebraicGeometry.QuasiSeparated f] → (AlgebraicGeometry.Scheme.Hom.normalization f).OpenCover

This is the open cover of f.normalization by Spec of integral closures of Γ(Y, U) in Γ(X, f ⁻¹ U) where U ranges over all affine opens.

Defined in
Mathlib.AlgebraicGeometry.Normalization
Cited by
9 results in Mathlib
Foundations
Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.QuasiCompactAlgebraicGeometry.QuasiSeparated
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.Hom.toNormalization · cited by 28Hom.toNormalizationAlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization · cited by 6Hom.toNormalization_fromN…AlgebraicGeometry.Scheme.Hom.normalizationObjIso · cited by 6Hom.normalizationObjIsoAlgebraicGeometry.Scheme.Hom.ι_fromNormalization · cited by 4Hom.ι_fromNormalizationAlgebraicGeometry.Scheme.Hom.ι_toNormalization · cited by 2Hom.ι_toNormalizationAlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc · cited by 2Hom.ι_toNormalization_ass…AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage · cited by 2Hom.toNormalization_app_p…AlgebraicGeometry.Scheme.Hom.fromNormalization_preimage · cited by 1Hom.fromNormalization_pre…AlgebraicGeometry.Scheme.Hom.fromNormalization_app · cited by 1Hom.fromNormalization_appAlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc · cited by 0Hom.ι_fromNormalization_a…AlgebraicGeometry.Scheme.Hom.normalization.hom_ext · cited by 0normalization.hom_extQuiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Scheme.OpenCover · cited by 207Scheme.OpenCoverAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…AlgebraicGeometry.QuasiSeparated · cited by 52AlgebraicGeometry.QuasiSe…AlgebraicGeometry.Scheme.Hom.normalization · cited by 41Hom.normalizationAlgebraicGeometry.Scheme.Cover.RelativeGluingData.cover · cited by 4RelativeGluingData.coverAlgebraicGeometry.Scheme.Hom.normalizationGlueData · cited by 3Hom.normalizationGlueDataHom.normalizationOpenCoverCITED BYCITES

Cites8

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Cited by11

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