Theorems · Theorem · number theory
NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff
∀ {k : Type u_1} [inst : Field k] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra k K] {σ : Gal(K/k)} {φ : K →+* ℂ},
NumberField.ComplexEmbedding.IsConj φ σ →
(NumberField.InfinitePlace.IsUnramified k (NumberField.InfinitePlace.mk φ) ↔ σ = 1)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Algebra.algebraMapproof · cited by 4,706
- AlgEquivstatement and proof · cited by 1,681
- RingHom.compproof · cited by 899
- NumberField.InfinitePlaceproof · cited by 604
- NumberField.InfinitePlace.IsRealproof · cited by 301
- not_iff_notproof · cited by 159
- NumberField.InfinitePlace.mkstatement and proof · cited by 56
- NumberField.InfinitePlace.comapproof · cited by 55
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConjproof · cited by 1
- NumberField.InfinitePlace.IsUnramified.stabilizer_eq_botproof · cited by 0