Theorems · Definition · number theory
NumberField.InfinitePlace.Completion.ringEquivComplexOfIsComplex
{K : Type u_1} → [inst : Field K] → {v : NumberField.InfinitePlace K} → v.IsComplex → v.Completion ≃+* ℂThe ring isomorphism v.Completion ≃+* ℂ, when v is complex, given by the bijection
v.Completion →+* ℂ.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Complexstatement · cited by 5,565
- RingEquivstatement · cited by 1,147
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsComplexstatement and proof · cited by 272
- NumberField.InfinitePlace.Completionstatement · cited by 69
- RingEquiv.ofBijectiveproof · cited by 24
- NumberField.InfinitePlace.Completion.extensionEmbeddingproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.IsUnramified.finrank_eq_oneproof · cited by 3
- NumberField.InfinitePlace.IsRamified.finrank_eq_twoproof · cited by 3
- NumberField.InfiniteAdeleRing.ringEquiv_mixedSpaceproof · cited by 2
- NumberField.InfinitePlace.Completion.isometryEquivComplexOfIsComplexproof · cited by 0
- NumberField.InfinitePlace.Completion.ringEquivComplexOfIsComplex_applystatement · cited by 0
- NumberField.InfinitePlace.Completion.ringEquivComplexOfIsComplex.congr_simpstatement and proof · cited by 0