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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsFinite.of_isProper_of_locallyQuasiFinite

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsProper f] [AlgebraicGeometry.LocallyQuasiFinite f],
  AlgebraicGeometry.IsFinite f
Defined in
Mathlib.AlgebraicGeometry.ZariskisMainTheorem
Cited by
2 results in Mathlib
Foundations
Depth 238 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsProperAlgebraicGeometry.LocallyQuasiFinite
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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AlgebraicGeometry.IsFinite.iff_isProper_and_locallyQuasiFinite · cited by 2IsFinite.iff_isProper_and…AlgebraicGeometry.exists_isFinite_morphismRestrict_of_finite_preimage_singleton · cited by 1AlgebraicGeometry.exists_…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoAlgebraicGeometry.IsFinite · cited by 33AlgebraicGeometry.IsFiniteAlgebraicGeometry.LocallyQuasiFinite · cited by 29AlgebraicGeometry.Locally…AlgebraicGeometry.Scheme.Hom.toNormalization · cited by 28Hom.toNormalizationAlgebraicGeometry.IsIntegralHom · cited by 18AlgebraicGeometry.IsInteg…AlgebraicGeometry.IsProper · cited by 17AlgebraicGeometry.IsProperAlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization · cited by 6Hom.toNormalization_fromN…AlgebraicGeometry.isIso_iff_isOpenImmersion_and_surjective · cited by 2AlgebraicGeometry.isIso_i…AlgebraicGeometry.IsFinite.iff_isIntegralHom_and_locallyOfFiniteType · cited by 2IsFinite.iff_isIntegralHo…IsFinite.of_isProper_of_local…CITED BYCITES

Cites11

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Cited by2

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