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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsFinite.iff_isProper_and_locallyQuasiFinite

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y),
  AlgebraicGeometry.IsFinite f ↔ AlgebraicGeometry.IsProper f ∧ AlgebraicGeometry.LocallyQuasiFinite f

[Stacks Tag 02LS](https://stacks.math.columbia.edu/tag/02LS) ((1) <=> (3))

Defined in
Mathlib.AlgebraicGeometry.ZariskisMainTheorem
Cited by
2 results in Mathlib
Foundations
Depth 239 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.IsClosedImmersion.iff_isProper_and_mono · cited by 1IsClosedImmersion.iff_isP…AlgebraicGeometry.IsFinite.eq_proper_inf_locallyQuasiFinite · cited by 0IsFinite.eq_proper_inf_lo…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.IsFinite · cited by 33AlgebraicGeometry.IsFiniteAlgebraicGeometry.LocallyQuasiFinite · cited by 29AlgebraicGeometry.Locally…AlgebraicGeometry.IsProper · cited by 17AlgebraicGeometry.IsProperAlgebraicGeometry.IsFinite.of_isProper_of_locallyQuasiFinite · cited by 2IsFinite.of_isProper_of_l…IsFinite.iff_isProper_and_loc…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.