Theorems · Theorem · number theory
NumberField.IsCMField.isConj_complexConj
∀ (K : Type u_1) [inst : Field K] [inst_1 : CharZero K] [inst_2 : NumberField.IsCMField K] [inst_3 : Algebra.IsIntegral ℚ K] (φ : K →+* ℂ), NumberField.ComplexEmbedding.IsConj φ (NumberField.IsCMField.complexConj K)
The complex conjugation is the conjugation of any complex embedding of a CM-field.
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 2 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- AlgEquivproof · 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 and proof · cited by 38
- NumberField.ComplexEmbedding.IsConjstatement and proof · cited by 24
- NumberField.IsCMField.complexConjstatement · cited by 14
- NumberField.IsCMField.exists_isConjproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.complexEmbedding_complexConjproof · cited by 2
- NumberField.IsCMField.complexConj_apply_applyproof · cited by 1