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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.normalizationGlueData

{X Y : AlgebraicGeometry.Scheme} →
  (f : X ⟶ Y) →
    [AlgebraicGeometry.QuasiCompact f] →
      [AlgebraicGeometry.QuasiSeparated f] →
        AlgebraicGeometry.Scheme.Cover.RelativeGluingData (AlgebraicGeometry.Scheme.AffineZariskiSite.directedCover Y)

The diagram of affine schemes that we glue to form the normalization.

Defined in
Mathlib.AlgebraicGeometry.Normalization
Cited by
3 results in Mathlib
Foundations
Depth 187 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.normalization · cited by 41Hom.normalizationAlgebraicGeometry.Scheme.Hom.fromNormalization · cited by 28Hom.fromNormalizationAlgebraicGeometry.Scheme.Hom.normalizationDesc · cited by 10Hom.normalizationDescAlgebraicGeometry.Scheme.Hom.normalizationOpenCover · cited by 9Hom.normalizationOpenCoverAlgebraicGeometry.Scheme.Hom.normalizationDesc_comp · cited by 5Hom.normalizationDesc_compAlgebraicGeometry.Scheme.Hom.ι_fromNormalization · cited by 4Hom.ι_fromNormalizationAlgebraicGeometry.Scheme.Hom.fromNormalization_preimage · cited by 1Hom.fromNormalization_pre…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.PreZeroHypercover.I₀ · cited by 763PreZeroHypercover.I₀AlgebraicGeometry.IsOpenImmersion · cited by 476AlgebraicGeometry.IsOpenI…CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover · cited by 469ZeroHypercover.toPreZeroH…AlgebraicGeometry.Scheme.precoverage · cited by 336Scheme.precoverageAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…AlgebraicGeometry.QuasiSeparated · cited by 52AlgebraicGeometry.QuasiSe…AlgebraicGeometry.Scheme.Cover.RelativeGluingData · cited by 12Cover.RelativeGluingDataAlgebraicGeometry.Scheme.AffineZariskiSite.directedCover · cited by 9AffineZariskiSite.directe…AlgebraicGeometry.Scheme.AffineZariskiSite.relativeGluingData · cited by 5AffineZariskiSite.relativ…AlgebraicGeometry.Scheme.Hom.coequifibered_normalizationDiagramMap · cited by 1Hom.coequifibered_normali…Hom.normalizationGlueDataCITED BYCITES

Cites12

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Cited by7

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