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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt

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

A morphism f : X ⟶ Y is quasi-finite at x : X if the stalk map 𝒪_{X, x} ⟶ 𝒪_{Y, f x} is quasi-finite.

Defined in
Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite
Cited by
14 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus · cited by 6Hom.quasiFiniteLocusAlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersion · cited by 3Hom.quasiFiniteAt_comp_if…AlgebraicGeometry.Scheme.Hom.quasiFiniteAt · cited by 2Hom.quasiFiniteAtAlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff · cited by 2Hom.quasiFiniteAt_comp_iffAlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber · cited by 2Hom.quasiFiniteAt_iff_isO…AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiber · cited by 1QuasiFiniteAt.isClopen_si…AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAt · cited by 1QuasiFiniteAt.quasiFinite…AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAt · cited by 1AlgebraicGeometry.exists_…AlgebraicGeometry.exists_isFinite_morphismRestrict_of_finite_preimage_singleton · cited by 1AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_isIso_morphism…AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_mem_and_isIso_…AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff · cited by 0Hom.quasiFiniteAt_iffAlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_comp · cited by 0Hom.quasiFiniteLocus_compAlgebraicGeometry.Scheme.Hom.mem_quasiFiniteLocus · cited by 0Hom.mem_quasiFiniteLocusAlgebraicGeometry.Scheme.Hom.isOpen_quasiFiniteAt · cited by 0Hom.isOpen_quasiFiniteAtQuiver.Hom · cited by 32603Quiver.HomTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…CommRingCat.Hom.hom · cited by 432Hom.homAlgebraicGeometry.Scheme.Hom.stalkMap · cited by 82Hom.stalkMapRingHom.QuasiFinite · cited by 21RingHom.QuasiFiniteHom.QuasiFiniteAtCITED BYCITES

Cites11

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Cited by15

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