Theorems · Theorem · algebraic geometry

Ideal.finrank_fiber_eq_rankAtStalk

∀ {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] (p : Ideal R) [hp : p.IsPrime],
  Module.finrank p.ResidueField (p.Fiber M) = Module.rankAtStalk M { asIdeal := p, isPrime := hp }

Variant of Module.rankAtStalk_eq for better rewriting.

Defined in

Mathlib.RingTheory.Spectrum.Prime.FreeLocus

Cited by

1 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.FlatModule.FiniteIdeal.IsPrime