Theorems · Theorem · algebraic geometry

Module.rankAtStalk_baseChange

∀ {R : Type uR} {M : Type uM} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Flat R M]
  [Module.Finite R M] {S : Type u_1} [inst_5 : CommRing S] [inst_6 : Algebra R S] (p : PrimeSpectrum S),
  Module.rankAtStalk (TensorProduct R S M) p = Module.rankAtStalk M (PrimeSpectrum.comap (algebraMap R S) p)

Defined in: Mathlib.RingTheory.Spectrum.Prime.FreeLocus
Cited by: 4 results in Mathlib
Foundations: Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module Module.Flat Module.Finite CommRing Algebra

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Cites27

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

Modulestatement and proof · cited by 20,661
RingHom.idproof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Algebrastatement and proof · cited by 11,388
Algebra.algebraMapstatement and proof · cited by 4,706
LinearEquivproof · cited by 3,317
TensorProductstatement and proof · cited by 2,545
LinearEquiv.symmproof · cited by 1,461
Module.Finitestatement and proof · cited by 1,032
PrimeSpectrumstatement and proof · cited by 625
Ideal.primeComplproof · cited by 462

Cited by4

Results whose statement or proof uses this declaration.

Algebra.rankAtStalk_eq_of_isPushoutproof · cited by 3
Module.rankAtStalk_isBaseChangeproof · cited by 2
Module.rankAtStalk_tensorProduct_of_isScalarTowerproof · cited by 0
Algebra.IsFiniteSplit.exists_tensorProduct_of_etaleproof · cited by 0