Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.ramificationIdxIn_eq

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

Write n = p ^ (k + 1) * m where the prime p does not divide m, then the ramification index of p in ℚ(ζₙ) is p ^ k * (p - 1).

Defined in

Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal

Cited by

1 results in Mathlib

Foundations

Depth 325 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactFieldNumberFieldIsCyclotomicExtension