Theorems · Theorem · number theory
Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply
∀ {R : Type u_2} [inst : CommRing R] [inst_1 : Algebra R ℚ] [inst_2 : IsIntegralClosure R ℤ ℚ]
[inst_3 : IsDedekindDomain R] [inst_4 : IsFractionRing R ℚ] (v : IsDedekindDomain.HeightOneSpectrum R)
(x : ℤ_[↑(Rat.HeightOneSpectrum.primesEquiv v)]),
↑((Rat.HeightOneSpectrum.adicCompletionIntegers.padicIntEquiv v).symm x) =
(Rat.HeightOneSpectrum.adicCompletion.padicEquiv v).symm ↑xThe diagram
``
v.adicCompletionIntegers ℚ < -- ℤ_[primesEquiv v]
| |
| |
v v
v.adicCompletion ℚ < - ℚ_[primesEquiv v]
``
commutes.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Equivstatement · cited by 8,337
- Norm.normstatement · cited by 5,413
- Nat.Primestatement · cited by 2,059
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- ValuationSubringstatement · cited by 187
- PadicIntstatement and proof · cited by 179
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.