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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsSeparated.of_valuativeCriterion

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.QuasiSeparated f],
  AlgebraicGeometry.ValuativeCriterion.Uniqueness f → AlgebraicGeometry.IsSeparated f

The valuative criterion for separated morphisms.

Defined in
Mathlib.AlgebraicGeometry.ValuativeCriterion
Cited by
1 results in Mathlib
Foundations
Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.QuasiSeparated
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Around this declaration

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

AlgebraicGeometry.IsSeparated.eq_valuativeCriterion · cited by 1IsSeparated.eq_valuativeC…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Category.assoc · cited by 6433Category.assocAlgebra.algebraMap · cited by 4706Algebra.algebraMapAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndAlgebraicGeometry.Spec.map · cited by 332Spec.mapCommRingCat.ofHom · cited by 259CommRingCat.ofHomCategoryTheory.CommSq · cited by 158CategoryTheory.CommSqCategoryTheory.Limits.pullback.condition · cited by 122pullback.conditionCategoryTheory.Limits.pullback.diagonalObj · cited by 80pullback.diagonalObjCategoryTheory.IsPullback.of_hasPullback · cited by 70IsPullback.of_hasPullbackCategoryTheory.Limits.pullback.diagonal · cited by 67pullback.diagonalIsSeparated.of_valuativeCrite…CITED BYCITES

Cites37

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Cited by1

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