Mathlib Map

Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.normalization

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

Given f : X ⟶ Y, f.normalization is the relative normalization of Y in X.

Defined in
Mathlib.AlgebraicGeometry.Normalization
Cited by
41 results in Mathlib
Foundations
Depth 200 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.fromNormalization · cited by 28Hom.fromNormalizationAlgebraicGeometry.Scheme.Hom.toNormalization · cited by 28Hom.toNormalizationAlgebraicGeometry.Scheme.Hom.normalizationCoprodIso · cited by 15Hom.normalizationCoprodIsoAlgebraicGeometry.Scheme.Hom.normalizationDesc · cited by 10Hom.normalizationDescAlgebraicGeometry.Scheme.Hom.normalizationOpenCover · cited by 9Hom.normalizationOpenCoverAlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization · cited by 6Hom.toNormalization_fromN…AlgebraicGeometry.Scheme.Hom.normalizationObjIso · cited by 6Hom.normalizationObjIsoAlgebraicGeometry.Scheme.Hom.normalizationPullback · cited by 5Hom.normalizationPullbackAlgebraicGeometry.Scheme.Hom.normalizationDesc_comp · cited by 5Hom.normalizationDesc_compAlgebraicGeometry.Scheme.Hom.ι_fromNormalization · cited by 4Hom.ι_fromNormalizationAlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDesc · cited by 4Hom.toNormalization_norma…AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDesc_assoc · cited by 2Hom.toNormalization_norma…AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst · cited by 2Hom.toNormalization_norma…AlgebraicGeometry.Scheme.Hom.ι_toNormalization · cited by 2Hom.ι_toNormalizationAlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc · cited by 2Hom.ι_toNormalization_ass…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…AlgebraicGeometry.QuasiSeparated · cited by 52AlgebraicGeometry.QuasiSe…AlgebraicGeometry.Scheme.Cover.RelativeGluingData.glued · cited by 7RelativeGluingData.gluedAlgebraicGeometry.Scheme.Hom.normalizationGlueData · cited by 3Hom.normalizationGlueDataHom.normalizationCITED BYCITES

Cites6

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

Cited by48

Results whose statement or proof uses this declaration.