Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.IsProper
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism is proper if it is separated, universally closed and locally of finite type.
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by19
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsProper.of_compstatement and proof · cited by 3
- AlgebraicGeometry.IsFinite.iff_isProper_and_locallyQuasiFinitestatement and proof · cited by 2
- AlgebraicGeometry.isProper_eqstatement · cited by 2
- AlgebraicGeometry.IsFinite.of_isProper_of_locallyQuasiFinitestatement and proof · cited by 2
- AlgebraicGeometry.isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosedstatement and proof · cited by 1
- AlgebraicGeometry.IsFinite.eq_isProper_inf_isAffineHomstatement and proof · cited by 1
- AlgebraicGeometry.exists_finite_imageι_comp_morphismRestrict_of_finite_image_preimagestatement and proof · cited by 1
- AlgebraicGeometry.exists_isFinite_morphismRestrict_of_finite_preimage_singletonstatement and proof · cited by 1
- AlgebraicGeometry.IsClosedImmersion.iff_isProper_and_monostatement and proof · cited by 1
- AlgebraicGeometry.isProper_iffstatement and proof · cited by 1
- AlgebraicGeometry.IsProper.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.IsProper.eq_valuativeCriterionstatement · cited by 1