Theorems · Theorem · number theory

NumberField.InfinitePlace.IsUnramified.finrank_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} [inst_3 : w.LiesOver v],
  NumberField.InfinitePlace.IsUnramified K w → Module.finrank v.Completion w.Completion = 1

If w is an unramified place over v then w.Completion has v.Completion dimension one.

Defined in: Mathlib.NumberTheory.NumberField.Completion.Ramification
Cited by: 3 results in Mathlib
Foundations: Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra NumberField.InfinitePlace.LiesOver

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Cites38

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

DFunLike.coeproof · cited by 62,936
Realproof · cited by 25,697
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Complexproof · cited by 5,565
Algebra.algebraMapproof · cited by 4,706
Module.finrankstatement · cited by 1,770
Complex.ofRealproof · cited by 1,654
RingHom.compproof · cited by 899
NumberField.InfinitePlacestatement and proof · cited by 604
RingHom.extproof · cited by 331
NumberField.InfinitePlace.IsRealproof · cited by 301

Cited by3

Results whose statement or proof uses this declaration.

NumberField.InfinitePlace.inertiaDeg_eq_oneproof · cited by 1
NumberField.InfinitePlace.Completion.finrank_eq_one_of_isUnramifiedproof · cited by 0
NumberField.InfinitePlace.mult_mul_finrankproof · cited by 0