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Theorems · Definition · number theory

NumberField.InfinitePlace.IsUnramified

(k : Type u_1) →
  [inst : Field k] → {K : Type u_2} → [inst_1 : Field K] → [Algebra k K] → NumberField.InfinitePlace K → Prop

An infinite place is unramified in a field extension if the restriction has the same multiplicity.

Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
Cited by
35 results in Mathlib
Foundations
Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.InfinitePlace.IsRamified · cited by 18InfinitePlace.IsRamifiedNumberField.InfinitePlace.IsUnramifiedIn · cited by 8InfinitePlace.IsUnramifie…NumberField.InfinitePlace.unramifiedPlacesOver · cited by 7InfinitePlace.unramifiedP…NumberField.InfinitePlace.isUnramified_iff · cited by 6InfinitePlace.isUnramifie…IsUnramifiedAtInfinitePlaces.isUnramified · cited by 4IsUnramifiedAtInfinitePla…NumberField.InfinitePlace.not_isUnramified_iff · cited by 4InfinitePlace.not_isUnram…NumberField.InfinitePlace.isUnramifiedIn_comap · cited by 4InfinitePlace.isUnramifie…NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_two · cited by 3InfinitePlace.not_isUnram…NumberField.InfinitePlace.even_card_aut_of_not_isUnramified · cited by 3InfinitePlace.even_card_a…NumberField.InfinitePlace.IsUnramified.eq · cited by 3IsUnramified.eqNumberField.InfinitePlace.IsUnramified.finrank_eq_one · cited by 3IsUnramified.finrank_eq_o…NumberField.InfinitePlace.card_stabilizer · cited by 2InfinitePlace.card_stabil…NumberField.InfinitePlace.even_finrank_of_not_isUnramified · cited by 2InfinitePlace.even_finran…NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff · cited by 2IsConj.isUnramified_mk_iffNumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_one · cited by 2InfinitePlace.isUnramifie…Algebra · cited by 11388AlgebraField · cited by 7404FieldAlgebra.algebraMap · cited by 4706Algebra.algebraMapNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.mult · cited by 107InfinitePlace.multNumberField.InfinitePlace.comap · cited by 55InfinitePlace.comapInfinitePlace.IsUnramifiedCITED BYCITES

Cites6

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Cited by40

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