Theorems · Theorem · number theory

IsDedekindDomain.HeightOneSpectrum.uniformContinuous_algebraMap_liesOver

∀ {A : Type u_1} (K : Type u_2) (L : Type u_3) {B : Type u_4} [inst : CommRing A] [inst_1 : IsDedekindDomain A]
  [inst_2 : CommRing B] [inst_3 : IsDedekindDomain B] [inst_4 : Algebra A B] [Module.IsTorsionFree A B]
  [inst_6 : Field K] [inst_7 : Field L] [inst_8 : Algebra K L] [inst_9 : Algebra A K] [inst_10 : IsFractionRing A K]
  [inst_11 : Algebra A L] [IsScalarTower A K L] [inst_13 : Algebra B L] [inst_14 : IsFractionRing B L]
  [IsScalarTower A B L] (v : IsDedekindDomain.HeightOneSpectrum A) (w : IsDedekindDomain.HeightOneSpectrum B)
  [w.asIdeal.LiesOver v.asIdeal],
  UniformContinuous
    ⇑(algebraMap (WithVal (IsDedekindDomain.HeightOneSpectrum.valuation K v))
        (WithVal (IsDedekindDomain.HeightOneSpectrum.valuation L w)))

Defined in

Mathlib.NumberTheory.RamificationInertia.Valuation

Cited by

0 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDedekindDomainCommRingIsDedekindDomainAlgebraModule.IsTorsionFreeFieldFieldAlgebraAlgebraIsFractionRingAlgebraIsScalarTowerAlgebraIsFractionRingIsScalarTowerIdeal.LiesOver