Theorems · Theorem · number theory

IsUnramifiedAt.of_liesOver_of_ne_bot

∀ (R : Type u_1) {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
  [inst_3 : Algebra R S] [inst_4 : Algebra S T] [inst_5 : Algebra R T] [IsScalarTower R S T] (p : Ideal S) (P : Ideal T)
  [P.LiesOver p] [inst_8 : p.IsPrime] [inst_9 : P.IsPrime] [Algebra.IsUnramifiedAt R P] [Algebra.EssFiniteType R S]
  [Algebra.EssFiniteType R T] [IsDedekindDomain S],
  P.primeCompl ≤ nonZeroDivisors T → (p ≠ ⊥ → P ≠ ⊥) → Algebra.IsUnramifiedAt R p

Defined in

Mathlib.NumberTheory.RamificationInertia.Unramified

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTowerIdeal.LiesOverIdeal.IsPrimeIdeal.IsPrimeAlgebra.IsUnramifiedAtAlgebra.EssFiniteTypeAlgebra.EssFiniteTypeIsDedekindDomain