Theorems · Definition · number theory
Rat.HeightOneSpectrum.adicCompletion.padicEquiv
{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) →
IsDedekindDomain.HeightOneSpectrum.adicCompletion ℚ v ≃A[ℚ] ℚ_[↑(Rat.HeightOneSpectrum.primesEquiv v)]The continuous ℚ-algebra isomorphism between v.adicCompletion ℚ and ℚ_[primesEquiv v].
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Equivstatement · cited by 8,337
- Nat.Primestatement · cited by 2,059
- RingEquivproof · cited by 1,147
- IsFractionRingstatement and proof · cited by 738
- Homeomorphproof · cited by 725
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- Padicstatement and proof · cited by 151
- IsIntegralClosurestatement and proof · cited by 146
Cited by6
Results whose statement or proof uses this declaration.
- Padic.adicCompletionEquivproof · cited by 2
- Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_applystatement · cited by 1
- Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOnstatement and proof · cited by 0
- Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_applystatement · cited by 0
- PadicInt.coe_adicCompletionIntegersEquiv_applyproof · cited by 0
- PadicInt.coe_adicCompletionIntegersEquiv_symm_applyproof · cited by 0