Theorems · Definition · number theory

NumberField.InfinitePlace.orbitRelEquiv

{k : Type u_1} →
  [inst : Field k] →
    {K : Type u_2} →
      [inst_1 : Field K] →
        [inst_2 : Algebra k K] →
          [IsGalois k K] →
            Quotient (MulAction.orbitRel Gal(K/k) (NumberField.InfinitePlace K)) ≃ NumberField.InfinitePlace k

The orbits of infinite places under the action of the Galois group are indexed by the infinite places of the base field.

Defined in: Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
Cited by: 1 results in Mathlib
Foundations: Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra IsGalois

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites10

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
Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapproof · cited by 4,706
AlgEquivstatement · cited by 1,681
NumberField.InfinitePlacestatement and proof · cited by 604
IsGaloisstatement and proof · cited by 149
MulAction.orbitRelstatement · cited by 114
Equiv.ofBijectiveproof · cited by 70
NumberField.InfinitePlace.comapproof · cited by 55

Cited by1

Results whose statement or proof uses this declaration.

NumberField.InfinitePlace.orbitRelEquiv_apply_mk''statement · cited by 0