Theorems · Definition · number theory
NumberField.IsCMField.complexConj
(K : Type u_1) →
[inst : Field K] →
[inst_1 : CharZero K] →
[NumberField.IsCMField K] → [Algebra.IsIntegral ℚ K] → Gal(K/↥(NumberField.maximalRealSubfield K))The complex conjugation of the CM-field K.
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement · cited by 1,681
- CharZerostatement and proof · cited by 932
- Subfieldstatement · cited by 303
- Algebra.IsIntegralstatement and proof · cited by 224
- NumberField.IsCMFieldstatement and proof · cited by 45
- NumberField.maximalRealSubfieldstatement · cited by 38
Cited by16
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.unitsComplexConjproof · cited by 5
- NumberField.IsCMField.ringOfIntegersComplexConjproof · cited by 3
- NumberField.IsCMField.isConj_complexConjstatement · cited by 2
- NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iffstatement · cited by 2
- NumberField.IsCMField.complexEmbedding_complexConjstatement · cited by 2
- NumberField.IsCMField.orderOf_complexConjstatement and proof · cited by 1
- NumberField.IsCMField.zpowers_complexConj_eq_topstatement and proof · cited by 1
- NumberField.IsCMField.coe_ringOfIntegersComplexConjstatement · cited by 1
- NumberField.IsCMField.complexConj_apply_applystatement · cited by 1
- NumberField.IsCMField.complexConj_eq_self_iffstatement and proof · cited by 1
- NumberField.IsCMField.complexConj_ne_onestatement · cited by 1
- NumberField.IsCMField.complexConj_torsionstatement and proof · cited by 1