Theorems · Theorem · number theory

NumberField.InfinitePlace.inertiaDeg_eq_one

∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
  {v : NumberField.InfinitePlace K} {w : NumberField.InfinitePlace L},
  w ∈ NumberField.InfinitePlace.unramifiedPlacesOver L v → v.inertiaDeg w = 1

Defined in: Mathlib.NumberTheory.NumberField.Completion.Ramification
Cited by: 1 results in Mathlib
Foundations: Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra

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.

Setstatement · cited by 53,352
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
NumberField.InfinitePlacestatement and proof · cited by 604
Set.mem_ofPredproof · cited by 104
NumberField.InfinitePlace.LiesOverproof · cited by 25
NumberField.InfinitePlace.unramifiedPlacesOverstatement and proof · cited by 7
NumberField.InfinitePlace.inertiaDegstatement · cited by 5
NumberField.InfinitePlace.IsUnramified.finrank_eq_oneproof · cited by 3
NumberField.InfinitePlace.inertiaDeg_eq_finrankproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

NumberField.InfinitePlace.sum_inertiaDeg_eq_finrankproof · cited by 0