Theorems · Theorem · number theory

NumberField.HeightOneSpectrum.adicAbv_def

∀ (K : Type u_1) [inst : Field K] {R : Type u_2} [inst_1 : CommRing R] [inst_2 : Algebra R K]
  [inst_3 : IsDedekindDomain R] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R)
  [inst_5 : Module.Finite ℤ R] [inst_6 : Module.Free ℤ R] {x : K},
  (NumberField.HeightOneSpectrum.adicAbv K v) x =
    ↑((WithZeroMulInt.toNNReal ⋯) ((IsDedekindDomain.HeightOneSpectrum.valuation K v) x))

Defined in: Mathlib.NumberTheory.NumberField.Completion.FinitePlace
Cited by: 4 results in Mathlib
Foundations: Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field CommRing Algebra IsDedekindDomain IsFractionRing Module.Finite Module.Free

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Cites24

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

DFunLike.coestatement · cited by 62,936
Realstatement · cited by 25,697
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Idealstatement · cited by 4,748
NNRealstatement · cited by 4,310
NNReal.toRealstatement · cited by 1,260
Module.Finitestatement and proof · cited by 1,032
Multiplicativestatement · cited by 875
Valuationstatement · cited by 823
IsFractionRingstatement and proof · cited by 738

Cited by4

Results whose statement or proof uses this declaration.

NumberField.HeightOneSpectrum.embedding_mul_absNormproof · cited by 3
NumberField.FinitePlace.norm_embedding'proof · cited by 1
NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_defproof · cited by 0
NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_defproof · cited by 0