Theorems · Theorem · number theory

Ideal.ncard_primesOver_mul_ramificationIdxIn_mul_inertiaDegIn

∀ {A : Type u_1} [inst : CommRing A] [IsDomain A] (p : Ideal A) [p.IsPrime] (B : Type u_2) [inst_3 : CommRing B]
  [IsDomain B] [inst_5 : Algebra A B] [Module.Finite A B] [Module.Flat A B] (G : Type u_3) [inst_8 : Group G] [Finite G]
  [inst_10 : MulSemiringAction G B] [IsGaloisGroup G A B],
  (p.primesOver B).ncard * (p.ramificationIdxIn B * p.inertiaDegIn B) = Nat.card G

The form of the fundamental identity in the case of Galois extension.

Defined in

Mathlib.NumberTheory.RamificationInertia.Galois

Cited by

5 results in Mathlib

Foundations

Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainIdeal.IsPrimeCommRingIsDomainAlgebraModule.FiniteModule.FlatGroupFiniteMulSemiringActionIsGaloisGroup