Theorems · Theorem · number theory

NumberField.InfinitePlace.card_isUnramified

∀ (k : Type u_1) [inst : Field k] (K : Type u_2) [inst_1 : Field K] [inst_2 : Algebra k K] [inst_3 : NumberField K]
  [inst_4 : NumberField k] [IsGalois k K],
  {w | NumberField.InfinitePlace.IsUnramified k w}.card =
    {w | NumberField.InfinitePlace.IsUnramifiedIn K w}.card * Module.finrank k K

Defined in: Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
Cited by: 1 results in Mathlib
Foundations: Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra NumberField NumberField IsGalois

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

Finsetproof · cited by 13,712
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Set.Elemproof · cited by 7,166
Set.ofPredproof · cited by 6,101
Finset.sumproof · cited by 5,195
Algebra.algebraMapproof · cited by 4,706
mul_oneproof · cited by 3,885
Finset.univstatement and proof · cited by 3,473
Finset.cardstatement and proof · cited by 2,327
Finset.sum_congrproof · cited by 2,323
Module.finrankstatement · cited by 1,770

Cited by1

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NumberField.InfinitePlace.card_eq_card_isUnramifiedInproof · cited by 1