Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one

∀ (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] {ζ : K} (hζ : IsPrimitiveRoot ζ (p ^ (k + 1))),
  (Ideal.span {hζ.toInteger - 1}).ramificationIdx ℤ = p ^ k * (p - 1)

Defined in

Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal

Cited by

4 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactFieldNumberFieldIsCyclotomicExtension