Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq

∀ (n : ℕ) [inst : NeZero n] (K : Type u_1) [inst_1 : Field K] [inst_2 : NumberField K]
  [hK : IsCyclotomicExtension {n} ℚ K] (σ : Gal(K/ℚ)) {x : NumberField.RingOfIntegers K},
  x ^ n = 1 → σ • x = x ^ (↑((IsCyclotomicExtension.Rat.galEquivZMod n K) σ)).val

Defined in: Mathlib.NumberTheory.NumberField.Cyclotomic.Galois
Cited by: 1 results in Mathlib
Foundations: Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NeZero Field NumberField IsCyclotomicExtension

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
Fieldstatement and proof · cited by 7,404
Unitsstatement · cited by 2,804
Units.valstatement and proof · cited by 1,966
AlgEquivstatement and proof · cited by 1,681
MulEquivstatement · cited by 1,142
ZModstatement · cited by 1,024
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement and proof · cited by 413
IsCyclotomicExtensionstatement and proof · cited by 220
FaithfulSMul.algebraMap_injectiveproof · cited by 198

Cited by1

Results whose statement or proof uses this declaration.

IsCyclotomicExtension.Rat.mem_zpowers_galEquivZMod_of_mem_stabilizerproof · cited by 1