Theorems · Theorem · commutative algebra

IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdx

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
  [inst_3 : p.IsPrime] (Rₚ : Type u_3) [inst_4 : CommRing Rₚ] [inst_5 : Algebra R Rₚ] [IsLocalization.AtPrime Rₚ p]
  [IsLocalRing Rₚ] (Sₚ : Type u_4) [inst_8 : CommRing Sₚ] [inst_9 : Algebra S Sₚ]
  [IsLocalization (Algebra.algebraMapSubmonoid S p.primeCompl) Sₚ] [inst_11 : Algebra Rₚ Sₚ] (P : Ideal S)
  [hPp : P.LiesOver p] [inst_12 : Algebra R Sₚ] [IsScalarTower R S Sₚ] [IsScalarTower R Rₚ Sₚ] [P.IsPrime],
  (Ideal.map (algebraMap S Sₚ) P).ramificationIdx Rₚ = P.ramificationIdx R

Defined in

Mathlib.RingTheory.Localization.AtPrime.Extension

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIdeal.IsPrimeCommRingAlgebraIsLocalization.AtPrimeIsLocalRingCommRingAlgebraIsLocalizationAlgebraIdeal.LiesOverAlgebraIsScalarTowerIsScalarTowerIdeal.IsPrime