Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.ramificationIdx_eq

∀ (n : ℕ) {m p k : ℕ} [hp : Fact (Nat.Prime p)] (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (P : Ideal (NumberField.RingOfIntegers K)) [hP₁ : P.IsPrime] [hP₂ : P.LiesOver (Ideal.span {↑p})]
  [IsCyclotomicExtension {n} ℚ K], n = p ^ (k + 1) * m → ¬p ∣ m → P.ramificationIdx ℤ = p ^ k * (p - 1)

Defined in

Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal

Cited by

0 results in Mathlib

Foundations

Depth 326 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactFieldNumberFieldIdeal.IsPrimeIdeal.LiesOverIsCyclotomicExtension