Theorems · Definition · number theory
NumberField.IsCMField.unitsComplexConj
(K : Type u_1) →
[inst : Field K] →
[inst_1 : CharZero K] →
[NumberField.IsCMField K] →
[Algebra.IsIntegral ℚ K] → (NumberField.RingOfIntegers K)ˣ ≃* (NumberField.RingOfIntegers K)ˣThe complex conjugation as an isomorphism of the units of K.
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 303 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Unitsstatement · cited by 2,804
- MulEquivstatement · cited by 1,142
- CharZerostatement and proof · cited by 932
- NumberField.RingOfIntegersstatement · cited by 413
- Algebra.IsIntegralstatement and proof · cited by 224
- AlgEquiv.toRingEquivproof · cited by 137
- MulEquivClass.toMulEquivproof · cited by 57
- NumberField.IsCMFieldstatement and proof · cited by 45
- Units.mapEquivproof · cited by 16
- NumberField.IsCMField.complexConjproof · cited by 14
- NumberField.RingOfIntegers.mapRingEquivproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.unitsMulComplexConjInvproof · cited by 9
- NumberField.IsCMField.unitsComplexConj_eq_self_iffstatement and proof · cited by 1
- NumberField.IsCMField.unitsComplexConj_torsionstatement and proof · cited by 1
- NumberField.IsCMField.unitsMulComplexConjInv_applystatement · cited by 1
- NumberField.IsCMField.unitsMulComplexConjInv_kerproof · cited by 1
- NumberField.IsCMField.unitsComplexConj.congr_simpstatement and proof · cited by 0