Theorems · Theorem · commutative algebra

IsFractionRing.stabilizerQuotientInertiaEquiv_mk

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] (G : Type u_3)
  [inst_3 : Group G] [inst_4 : Finite G] [inst_5 : MulSemiringAction G B] [inst_6 : SMulCommClass G A B] (P : Ideal A)
  (Q : Ideal B) [inst_7 : Q.IsPrime] [inst_8 : Q.LiesOver P] (K : Type u_4) (L : Type u_5) [inst_9 : Field K]
  [inst_10 : Field L] [inst_11 : Algebra (A ⧸ P) K] [inst_12 : Algebra (B ⧸ Q) L] [inst_13 : Algebra (A ⧸ P) L]
  [inst_14 : IsScalarTower (A ⧸ P) (B ⧸ Q) L] [inst_15 : Algebra K L] [inst_16 : IsScalarTower (A ⧸ P) K L]
  [inst_17 : Algebra.IsInvariant A B G] [inst_18 : IsFractionRing (A ⧸ P) K] [inst_19 : IsFractionRing (B ⧸ Q) L]
  (g : ↥(MulAction.stabilizer G Q)),
  (IsFractionRing.stabilizerQuotientInertiaEquiv G P Q K L) ↑g = (IsFractionRing.stabilizerHom G P Q K L) g

Defined in

Mathlib.RingTheory.Invariant.Basic

Cited by

0 results in Mathlib

Foundations

Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraGroupFiniteMulSemiringActionSMulCommClassIdeal.IsPrimeIdeal.LiesOverFieldFieldAlgebraAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerAlgebra.IsInvariantIsFractionRingIsFractionRing