Theorems · Definition · number theory

IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroMod

{R : Type u} →
  [inst : CommRing R] →
    [IsDedekindDomain R] →
      {K : Type v} →
        [inst_2 : Field K] →
          [inst_3 : Algebra R K] →
            [IsFractionRing R K] →
              IsDedekindDomain.HeightOneSpectrum R → (n : ℕ) → Kˣ ⧸ (powMonoidHom n).range →* Multiplicative (ZMod n)

The multiplicative v-adic valuation on Kˣ modulo n-th powers.

Defined in: Mathlib.RingTheory.DedekindDomain.SelmerGroup
Cited by: 2 results in Mathlib
Foundations: Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain Field Algebra IsFractionRing

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Cites23

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

DFunLike.coeproof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
MonoidHomstatement · cited by 3,629
Subgroupstatement · cited by 3,593
Unitsstatement · cited by 2,804
HasQuotient.Quotientstatement · cited by 2,301
ZModstatement · cited by 1,024
Multiplicativestatement · cited by 875
IsFractionRingstatement and proof · cited by 738
IsDedekindDomainstatement and proof · cited by 668

Cited by4

Results whose statement or proof uses this declaration.

IsDedekindDomain.selmerGroupproof · cited by 4
IsDedekindDomain.selmerGroup.valuationproof · cited by 1
IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroMod.congr_simpstatement and proof · cited by 0
IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eqstatement · cited by 0