Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_algebraMap
∀ (R S : Type u) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Module.Finite R S] [Module.Flat R S]
(x : PrimeSpectrum R),
AlgebraicGeometry.Scheme.Hom.finrank (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (algebraMap R S))) x =
Module.rankAtStalk S x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Algebra.algebraMapstatement and proof · cited by 4,706
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- Module.Finitestatement and proof · cited by 1,032
- AlgebraicGeometry.Specstatement and proof · cited by 626
- PrimeSpectrumstatement and proof · cited by 625
- AlgebraicGeometry.Spec.mapstatement · cited by 332
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