Theorems · Theorem · number theory

Ideal.inertiaDegIn_eq_inertiaDeg

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] (p : Ideal A)
  (P : Ideal B) [hPp : P.IsPrime] [hp : P.LiesOver p] (G : Type u_3) [inst_3 : Group G] [Finite G]
  [inst_5 : MulSemiringAction G B] [IsGaloisGroup G A B], p.inertiaDegIn B = P.inertiaDeg A

The inertiaDegIn is equal to any ramification index over the same ideal.

Defined in

Mathlib.NumberTheory.RamificationInertia.Galois

Cited by

11 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIdeal.IsPrimeIdeal.LiesOverGroupFiniteMulSemiringActionIsGaloisGroup