Theorems · Theorem · algebraic geometry

Module.rankAtStalk_tensorProduct_of_isScalarTower

∀ {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] (N : Type u_2)
  [inst_7 : AddCommGroup N] [inst_8 : Module R N] [inst_9 : Module S N] [inst_10 : IsScalarTower R S N]
  [Module.Finite S N] [Module.Flat S N] (p : PrimeSpectrum S),
  Module.rankAtStalk (TensorProduct R N M) p =
    Module.rankAtStalk N p * Module.rankAtStalk M (PrimeSpectrum.comap (algebraMap R S) p)

Defined in: Mathlib.RingTheory.Spectrum.Prime.FreeLocus
Cited by: 0 results in Mathlib
Foundations: Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module Module.Flat Module.Finite CommRing Algebra AddCommGroup Module Module IsScalarTower Module.Finite Module.Flat

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites17

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
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
IsScalarTowerstatement and proof · cited by 3,896
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
Module.Flatstatement and proof · cited by 279
PrimeSpectrum.comapstatement and proof · cited by 199

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.