Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → ↥X → PropA morphism f : X ⟶ Y is quasi-finite at x : X
if the stalk map 𝒪_{X, x} ⟶ 𝒪_{Y, f x} is quasi-finite.
- 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- CommRingCat.Hom.homproof · cited by 432
- AlgebraicGeometry.Scheme.Hom.stalkMapproof · cited by 82
- RingHom.QuasiFiniteproof · cited by 21
Cited by15
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.quasiFiniteLocusproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersionstatement · cited by 3
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAtstatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iffstatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiberstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAtstatement and proof · cited by 1
- AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalizationstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalizationstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iffstatement and proof · cited by 0