Theorems · Theorem · number theory
NumberField.HeightOneSpectrum.isNonarchimedean_adicAbv
∀ (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], IsNonarchimedean ⇑(NumberField.HeightOneSpectrum.adicAbv K v)The v-adic absolute value is nonarchimedean
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Module.Finitestatement and proof · cited by 1,032
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- AbsoluteValuestatement · cited by 363
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsNonarchimedeanstatement · cited by 77
Cited by5
Results whose statement or proof uses this declaration.
- NumberField.HeightOneSpectrum.adicAbv_add_le_maxproof · cited by 3
- NumberField.HeightOneSpectrum.adicAbv_intCast_le_oneproof · cited by 2
- NumberField.HeightOneSpectrum.adicAbv_natCast_le_oneproof · cited by 2
- NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbvproof · cited by 0