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Theorems · Inductive type · algebraic geometry

AlgebraicGeometry.IsProper

{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → Prop

A morphism is proper if it is separated, universally closed and locally of finite type.

Defined in
Mathlib.AlgebraicGeometry.Morphisms.Proper
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.

AlgebraicGeometry.IsProper.of_comp · cited by 3IsProper.of_compAlgebraicGeometry.IsFinite.iff_isProper_and_locallyQuasiFinite · cited by 2IsFinite.iff_isProper_and…AlgebraicGeometry.isProper_eq · cited by 2AlgebraicGeometry.isPrope…AlgebraicGeometry.IsFinite.of_isProper_of_locallyQuasiFinite · cited by 2IsFinite.of_isProper_of_l…AlgebraicGeometry.isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed · cited by 1AlgebraicGeometry.isCommM…AlgebraicGeometry.IsFinite.eq_isProper_inf_isAffineHom · cited by 1IsFinite.eq_isProper_inf_…AlgebraicGeometry.exists_finite_imageι_comp_morphismRestrict_of_finite_image_preimage · cited by 1AlgebraicGeometry.exists_…AlgebraicGeometry.exists_isFinite_morphismRestrict_of_finite_preimage_singleton · cited by 1AlgebraicGeometry.exists_…AlgebraicGeometry.IsClosedImmersion.iff_isProper_and_mono · cited by 1IsClosedImmersion.iff_isP…AlgebraicGeometry.isProper_iff · cited by 1AlgebraicGeometry.isPrope…AlgebraicGeometry.IsProper.casesOn · cited by 1IsProper.casesOnAlgebraicGeometry.IsProper.eq_valuativeCriterion · cited by 1IsProper.eq_valuativeCrit…AlgebraicGeometry.isCommMonObj_of_isProper_of_geometricallyIntegral · cited by 0AlgebraicGeometry.isCommM…AlgebraicGeometry.IsFinite.eq_proper_inf_locallyQuasiFinite · cited by 0IsFinite.eq_proper_inf_lo…AlgebraicGeometry.IsFinite.iff_isProper_and_isAffineHom · cited by 0IsFinite.iff_isProper_and…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.IsProperCITED BYCITES

Cites2

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

Cited by19

Results whose statement or proof uses this declaration.