Theorems · Definition · number theory
NumberField.ComplexEmbedding.IsConj
{K : Type u_1} →
[inst : Field K] → {k : Type u_2} → [inst_1 : Field k] → [inst_2 : Algebra k K] → (K →+* ℂ) → Gal(K/k) → PropIsConj φ σ states that σ : Gal(K/k) is the conjugation under the embedding φ : K →+* ℂ.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- AlgEquivstatement and proof · cited by 1,681
- RingHom.compproof · cited by 899
- RingHomClass.toRingHomproof · cited by 746
- NumberField.ComplexEmbedding.conjugateproof · cited by 40
Cited by24
Results whose statement or proof uses this declaration.
- NumberField.ComplexEmbedding.IsConj.eqstatement and proof · cited by 5
- NumberField.ComplexEmbedding.isConj_one_iffstatement · cited by 4
- NumberField.ComplexEmbedding.isConj_ne_one_iffstatement and proof · cited by 3
- NumberField.ComplexEmbedding.IsConj.ext_iffstatement and proof · cited by 3
- NumberField.ComplexEmbedding.isConj_apply_applystatement and proof · cited by 2
- NumberField.IsCMField.exists_isConjstatement · cited by 2
- NumberField.IsCMField.isConj_complexConjstatement and proof · cited by 2
- NumberField.ComplexEmbedding.IsConj.isReal_compstatement and proof · cited by 2
- NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iffstatement and proof · cited by 2
- NumberField.InfinitePlace.mem_stabilizer_mk_iffstatement and proof · cited by 2
- NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_twoproof · cited by 1
- NumberField.ComplexEmbedding.isConj_symmstatement · cited by 1