Theorems · Theorem · algebraic geometry

Module.rankAtStalk_isBaseChange

∀ {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} {Mₛ : Type u_2} [inst_5 : CommRing S] [inst_6 : Algebra R S]
  [inst_7 : AddCommGroup Mₛ] [inst_8 : Module R Mₛ] [inst_9 : Module S Mₛ] [inst_10 : IsScalarTower R S Mₛ]
  {f : M →ₗ[R] Mₛ},
  IsBaseChange S f →
    ∀ (p : PrimeSpectrum S), Module.rankAtStalk Mₛ p = Module.rankAtStalk M (PrimeSpectrum.comap (algebraMap R S) p)

Defined in: Mathlib.RingTheory.Spectrum.Prime.FreeLocus
Cited by: 2 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

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Cites18

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.idstatement and proof · 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
LinearMapstatement and proof · cited by 10,215
Algebra.algebraMapstatement and proof · cited by 4,706
IsScalarTowerstatement and proof · cited by 3,896
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

Cited by2

Results whose statement or proof uses this declaration.

Module.rankAtStalk_eq_of_le_of_finite_of_flatproof · cited by 1
Module.Free.away_of_finite_of_flat_of_rankAtStalk_constantproof · cited by 0