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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.PartialMap.isOver_toRationalMap_iff_of_isSeparated

∀ {X Y S : AlgebraicGeometry.Scheme} [inst : X.Over S] [inst_1 : Y.Over S] [AlgebraicGeometry.IsReduced X]
  [S.IsSeparated] {f : X.PartialMap Y},
  AlgebraicGeometry.Scheme.RationalMap.IsOver S f.toRationalMap ↔ AlgebraicGeometry.Scheme.PartialMap.IsOver S f
Defined in
Mathlib.AlgebraicGeometry.Birational.RationalMap
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Foundations
Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.Scheme.OverAlgebraicGeometry.Scheme.OverAlgebraicGeometry.IsReducedAlgebraicGeometry.Scheme.IsSeparated
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CategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compSetLike.coe · cited by 8199SetLike.coeCategoryTheory.Category.assoc · cited by 6433Category.assocAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.Scheme.Opens.toScheme · cited by 433Opens.toSchemeDense · cited by 359DenseAlgebraicGeometry.Scheme.Opens.ι · cited by 275Opens.ιAlgebraicGeometry.Scheme.homOfLE · cited by 103Scheme.homOfLEAlgebraicGeometry.Scheme.PartialMap · cited by 76Scheme.PartialMapCategoryTheory.over · cited by 76CategoryTheory.overAlgebraicGeometry.Scheme.PartialMap.domain · cited by 60PartialMap.domainAlgebraicGeometry.Scheme.PartialMap.hom · cited by 49PartialMap.homAlgebraicGeometry.IsDominant · cited by 43AlgebraicGeometry.IsDomin…AlgebraicGeometry.IsReduced · cited by 38AlgebraicGeometry.IsReduc…PartialMap.isOver_toRationalM…CITED BYCITES

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