Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_eq_finrank

∀ {R S : CommRingCat} {f : R ⟶ S},
  (CommRingCat.Hom.hom f).Finite →
    (CommRingCat.Hom.hom f).Flat →
      AlgebraicGeometry.Scheme.Hom.finrank (AlgebraicGeometry.Spec.map f) = (CommRingCat.Hom.hom f).finrank

Defined in: Mathlib.AlgebraicGeometry.Morphisms.FlatRank
Cited by: 6 results in Mathlib
Foundations: Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites44

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

DFunLike.coeproof · cited by 62,936
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Iso.homproof · cited by 7,684
CategoryTheory.Iso.invproof · cited by 6,514
CategoryTheory.ConcreteCategory.homproof · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
CommRingCatstatement and proof · 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

Cited by6

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.one_le_finrank_mapproof · cited by 1
AlgebraicGeometry.Scheme.Hom.finrank_eq_one_of_isIsoproof · cited by 1
AlgebraicGeometry.Scheme.Hom.one_le_finrank_iff_surjectiveproof · cited by 0
AlgebraicGeometry.Scheme.Hom.isIso_iff_finrank_eqproof · cited by 0
AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_algebraMapproof · cited by 0
AlgebraicGeometry.Scheme.Hom.isLocallyConstant_finrankproof · cited by 0