Theorems · Theorem · number theory

NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConj

∀ {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.IsUnramified k (NumberField.InfinitePlace.mk φ) ↔
    ∀ (σ : Gal(K/k)), NumberField.ComplexEmbedding.IsConj φ σ → σ = 1

Defined in: Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
Cited by: 1 results in Mathlib
Foundations: Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra IsGalois

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NumberField.InfinitePlaceproof · cited by 604
RingHom.toAlgebraproof · cited by 337

Cited by1

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NumberField.InfinitePlace.isUnramified_iff_stabilizer_eq_botproof · cited by 1