Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.finrank
{X S : AlgebraicGeometry.Scheme} → (X ⟶ S) → ↥S → ℕThe rank of a morphism f : X ⟶ S of schemes at a point s : S. When f is finite,
flat and locally of finite presentation, this is a locally constant function (see
AlgebraicGeometry.isLocallyConstant_finrank).
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CategoryTheory.Limits.pullback.sndproof · cited by 637
- AlgebraicGeometry.Scheme.AffineCover.fproof · cited by 24
- AlgebraicGeometry.Scheme.affineOpenCoverproof · cited by 8
- AlgebraicGeometry.Scheme.AffineCover.idxproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.finrank_comp_left_of_isIsostatement and proof · cited by 7
- AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_eq_finrankstatement · cited by 6
- AlgebraicGeometry.Scheme.Hom.finrank_pullback_sndstatement and proof · cited by 6
- AlgebraicGeometry.Scheme.Hom.one_le_finrank_mapstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.finrank_eq_one_of_isIsostatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.finrank_of_isPullbackstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.one_le_finrank_iff_surjectivestatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_algebraMapstatement · cited by 0
- AlgebraicGeometry.Scheme.Hom.finrank_pullback_fststatement · cited by 0
- AlgebraicGeometry.Scheme.Hom.isIso_iff_finrank_eqstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.isLocallyConstant_finrankstatement and proof · cited by 0