Theorems · Theorem · number theory
NumberField.IsCMField.zpowers_complexConj_eq_top
∀ (K : Type u_1) [inst : Field K] [inst_1 : CharZero K] [inst_2 : NumberField.IsCMField K] [inst_3 : Algebra.IsIntegral ℚ K], Subgroup.zpowers (NumberField.IsCMField.complexConj K) = ⊤
The complex conjugation generates the Galois group of K/K⁺.
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- CharZerostatement and proof · cited by 932
- Nat.cardproof · cited by 844
- Subfieldstatement · cited by 303
- Algebra.IsIntegralstatement and proof · cited by 224
- Subgroup.zpowersstatement and proof · cited by 204
- NumberField.IsCMFieldstatement and proof · cited by 45
- NumberField.maximalRealSubfieldstatement and proof · cited by 38
- IsGalois.card_aut_eq_finrankproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.complexConj_eq_self_iffproof · cited by 1