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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsProper.eq_valuativeCriterion

@AlgebraicGeometry.IsProper =
  AlgebraicGeometry.ValuativeCriterion ⊓ @AlgebraicGeometry.QuasiCompact ⊓ @AlgebraicGeometry.QuasiSeparated ⊓
    @AlgebraicGeometry.LocallyOfFiniteType

The valuative criterion for proper morphisms.

Defined in
Mathlib.AlgebraicGeometry.ValuativeCriterion
Cited by
1 results in Mathlib
Foundations
Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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AlgebraicGeometry.IsProper.of_valuativeCriterion · cited by 0IsProper.of_valuativeCrit…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…AlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…AlgebraicGeometry.LocallyOfFiniteType · cited by 59AlgebraicGeometry.Locally…inf_assoc · cited by 53inf_assocAlgebraicGeometry.QuasiSeparated · cited by 52AlgebraicGeometry.QuasiSe…AlgebraicGeometry.UniversallyClosed · cited by 24AlgebraicGeometry.Univers…AlgebraicGeometry.IsProper · cited by 17AlgebraicGeometry.IsProperAlgebraicGeometry.ValuativeCriterion.Existence · cited by 11ValuativeCriterion.Existe…AlgebraicGeometry.ValuativeCriterion.Uniqueness · cited by 7ValuativeCriterion.Unique…AlgebraicGeometry.ValuativeCriterion · cited by 6AlgebraicGeometry.Valuati…AlgebraicGeometry.isProper_eq · cited by 2AlgebraicGeometry.isPrope…AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterion · cited by 2UniversallyClosed.eq_valu…AlgebraicGeometry.IsSeparated.eq_valuativeCriterion · cited by 1IsSeparated.eq_valuativeC…IsProper.eq_valuativeCriterionCITED BYCITES

Cites16

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Cited by1

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