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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsProper.of_valuativeCriterion

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.QuasiCompact f] [AlgebraicGeometry.QuasiSeparated f]
  [AlgebraicGeometry.LocallyOfFiniteType f], AlgebraicGeometry.ValuativeCriterion f → AlgebraicGeometry.IsProper f

The valuative criterion for proper morphisms.

Defined in
Mathlib.AlgebraicGeometry.ValuativeCriterion
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Foundations
Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.QuasiCompactAlgebraicGeometry.QuasiSeparatedAlgebraicGeometry.LocallyOfFiniteType
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Around this declaration

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Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…AlgebraicGeometry.LocallyOfFiniteType · cited by 59AlgebraicGeometry.Locally…AlgebraicGeometry.QuasiSeparated · cited by 52AlgebraicGeometry.QuasiSe…AlgebraicGeometry.IsProper · cited by 17AlgebraicGeometry.IsProperAlgebraicGeometry.ValuativeCriterion · cited by 6AlgebraicGeometry.Valuati…AlgebraicGeometry.IsProper.eq_valuativeCriterion · cited by 1IsProper.eq_valuativeCrit…IsProper.of_valuativeCriterionCITED BYCITES

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