Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.mem_zpowers_galEquivZMod_of_mem_stabilizer

∀ (n : ℕ) [inst : NeZero n] (K : Type u_1) [inst_1 : Field K] [inst_2 : NumberField K]
  [hK : IsCyclotomicExtension {n} ℚ K] (p : ℕ) [hp : Fact (Nat.Prime p)] (P : Ideal (NumberField.RingOfIntegers K))
  [P.IsMaximal] [P.LiesOver (Ideal.span {↑p})] (hn : p.Coprime n) {σ : Gal(K/ℚ)},
  σ ∈ MulAction.stabilizer Gal(K/ℚ) P →
    (IsCyclotomicExtension.Rat.galEquivZMod n K) σ ∈ Subgroup.zpowers (ZMod.unitOfCoprime p hn)

Defined in

Mathlib.NumberTheory.NumberField.Cyclotomic.Galois

Cited by

1 results in Mathlib

Foundations

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

Assumes

NeZeroFieldNumberFieldIsCyclotomicExtensionFactIdeal.IsMaximalIdeal.LiesOver