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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.UniversallyClosed.of_valuativeCriterion

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.QuasiCompact f],
  AlgebraicGeometry.ValuativeCriterion.Existence f → AlgebraicGeometry.UniversallyClosed f

The valuative criterion for universally closed morphisms.

Defined in
Mathlib.AlgebraicGeometry.ValuativeCriterion
Cited by
1 results in Mathlib
Foundations
Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.QuasiCompact
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.IsSeparated.of_valuativeCriterion · cited by 1IsSeparated.of_valuativeC…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…AlgebraicGeometry.UniversallyClosed · cited by 24AlgebraicGeometry.Univers…AlgebraicGeometry.ValuativeCriterion.Existence · cited by 11ValuativeCriterion.Existe…AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterion · cited by 2UniversallyClosed.eq_valu…UniversallyClosed.of_valuativ…CITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.