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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.partialIso

{X U : AlgebraicGeometry.Scheme} →
  (f : U ⟶ X) → [AlgebraicGeometry.IsOpenImmersion f] → [AlgebraicGeometry.IsDominant f] → U.PartialIso X

A dominant open immersion f : U ⟶ X induces a partial isomorphism between U and X.

Defined in
Mathlib.AlgebraicGeometry.Birational.Birational
Cited by
5 results in Mathlib
Foundations
Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsOpenImmersionAlgebraicGeometry.IsDominant
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.partialIso_iso · cited by 1Hom.partialIso_isoAlgebraicGeometry.Scheme.Hom.partialIso_target · cited by 0Hom.partialIso_targetAlgebraicGeometry.Scheme.Hom.birational · cited by 0Hom.birationalAlgebraicGeometry.Scheme.Hom.birationalOver · cited by 0Hom.birationalOverAlgebraicGeometry.Scheme.Hom.partialIso_source · cited by 0Hom.partialIso_sourceQuiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.IsOpenImmersion · cited by 476AlgebraicGeometry.IsOpenI…AlgebraicGeometry.Scheme.Hom.opensRange · cited by 113Hom.opensRangeAlgebraicGeometry.IsDominant · cited by 43AlgebraicGeometry.IsDomin…AlgebraicGeometry.Scheme.PartialIso · cited by 32Scheme.PartialIsoAlgebraicGeometry.Scheme.Hom.isoOpensRange · cited by 17Hom.isoOpensRangeAlgebraicGeometry.Scheme.Opens.partialIsoOfDense · cited by 8Opens.partialIsoOfDenseAlgebraicGeometry.Scheme.PartialIso.trans' · cited by 4PartialIso.trans'AlgebraicGeometry.Scheme.PartialIso.ofIso · cited by 4PartialIso.ofIsoAlgebraicGeometry.Scheme.Hom.denseRange · cited by 4Hom.denseRangeHom.partialIsoCITED BYCITES

Cites11

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Cited by5

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