Theorems · Theorem · number theory

Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn

∀ {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),
  Set.BijOn ⇑(Rat.HeightOneSpectrum.adicCompletion.padicEquiv v)
    ↑(IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers ℚ v)
    ↑(PadicInt.subring ↑(Rat.HeightOneSpectrum.primesEquiv v))

Defined in: Mathlib.NumberTheory.Padics.HeightOneSpectrum
Cited by: 0 results in Mathlib
Foundations: Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Algebra IsIntegralClosure IsDedekindDomain IsFractionRing

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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
SetLike.coestatement and proof · cited by 8,199
Nat.Primestatement · cited by 2,059
IsFractionRingstatement and proof · cited by 738
IsDedekindDomainstatement and proof · cited by 668
Subringstatement · cited by 602
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
Function.Injective.injOnproof · cited by 280
ValuationSubringstatement · cited by 187

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