Theorems · Definition · number theory

NumberField.InfinitePlace.placesOver

{K : Type u_4} →
  (L : Type u_5) →
    [inst : Field K] →
      [inst_1 : Field L] → [Algebra K L] → NumberField.InfinitePlace K → Set (NumberField.InfinitePlace L)

The set of infinite places of L that lie above a given infinite place of K.

Defined in: Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
Cited by: 2 results in Mathlib
Foundations: Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Set.ofPredproof · cited by 6,101
NumberField.InfinitePlacestatement and proof · cited by 604
NumberField.InfinitePlace.LiesOverproof · cited by 25

Cited by2

Results whose statement or proof uses this declaration.

NumberField.InfinitePlace.union_ramifiedPlacesOver_unramifiedPlacesOverstatement · cited by 1
NumberField.InfinitePlace.sum_inertiaDeg_eq_finrankstatement · cited by 0