Theorems · Theorem · algebraic geometry

Ideal.finrank_fiber_eq_finrank

∀ {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] [IsDomain R] (p : Ideal R) [inst_6 : p.IsPrime],
  Module.finrank p.ResidueField (p.Fiber M) = Module.finrank R M

Defined in: Mathlib.RingTheory.Spectrum.Prime.FreeLocus
Cited by: 1 results in Mathlib
Foundations: Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module Module.Flat Module.Finite IsDomain Ideal.IsPrime

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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
Idealstatement and proof · cited by 4,748
TensorProductproof · cited by 2,545
IsDomainstatement and proof · cited by 2,196
Module.finrankstatement and proof · cited by 1,770
Module.Finitestatement and proof · cited by 1,032
Ideal.IsPrimestatement and proof · cited by 827
Ideal.primeComplstatement and proof · cited by 462
Localization.AtPrimestatement and proof · cited by 299
Module.Flatstatement and proof · cited by 279

Cited by1

Results whose statement or proof uses this declaration.

Ideal.sum_ramification_inertia_eq_finrankproof · cited by 1