Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.ramificationIdxIn_eq_of_prime_pow

∀ (p k : ℕ) [hp : Fact (Nat.Prime p)] (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  [hK : IsCyclotomicExtension {p ^ (k + 1)} ℚ K],
  (Ideal.span {↑p}).ramificationIdxIn (NumberField.RingOfIntegers K) = p ^ k * (p - 1)

Defined in

Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal

Cited by

1 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactFieldNumberFieldIsCyclotomicExtension