Theorems · Definition · number theory
IsDedekindDomain.selmerGroup.valuation
{R : Type u} →
[inst : CommRing R] →
[inst_1 : IsDedekindDomain R] →
{K : Type v} →
[inst_2 : Field K] →
[inst_3 : Algebra R K] →
[inst_4 : IsFractionRing R K] →
{S : Set (IsDedekindDomain.HeightOneSpectrum R)} →
{n : ℕ} → ↥IsDedekindDomain.selmerGroup →* ↑S → Multiplicative (ZMod n)The multiplicative v-adic valuations on K⟮S, n⟯ for all v ∈ S.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement and proof · cited by 7,166
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientstatement and proof · cited by 2,301
- ZModstatement · cited by 1,024
- Multiplicativestatement · cited by 875
Cited by1
Results whose statement or proof uses this declaration.
- IsDedekindDomain.selmerGroup.valuation_ker_eqstatement and proof · cited by 0