Theorems · Theorem · number theory
NumberField.InfinitePlace.exists_isConj_of_isRamified
∀ {k : Type u_1} [inst : Field k] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra k K] [IsGalois k K] {φ : K →+* ℂ},
NumberField.InfinitePlace.IsRamified k (NumberField.InfinitePlace.mk φ) → ∃ σ, NumberField.ComplexEmbedding.IsConj φ σ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Set.univproof · cited by 3,945
- AlgEquivstatement and proof · cited by 1,681
- MulAction.stabilizerproof · cited by 254
- IsGaloisstatement and proof · cited by 149
- NumberField.InfinitePlace.mkstatement and proof · cited by 56
- NumberField.ComplexEmbedding.IsConjstatement · cited by 24
- NumberField.InfinitePlace.IsRamifiedstatement and proof · cited by 18
- NumberField.InfinitePlace.mem_stabilizer_mk_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.exists_isConjproof · cited by 2