Theorems · Theorem · commutative algebra

IsFractionRing.stabilizerHom_surjective

∀ {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] [Finite G] [inst_5 : MulSemiringAction G B] [inst_6 : SMulCommClass G A B] (P : Ideal A)
  (Q : Ideal B) [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]
  [Algebra.IsInvariant A B G] [inst_18 : IsFractionRing (A ⧸ P) K] [inst_19 : IsFractionRing (B ⧸ Q) L],
  Function.Surjective ⇑(IsFractionRing.stabilizerHom G P Q K L)

The stabilizer subgroup of Q surjects onto Aut(Frac(B/Q)/Frac(A/P)).

Defined in

Mathlib.RingTheory.Invariant.Basic

Cited by

2 results in Mathlib

Foundations

Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraGroupFiniteMulSemiringActionSMulCommClassIdeal.IsPrimeIdeal.LiesOverFieldFieldAlgebraAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerAlgebra.IsInvariantIsFractionRingIsFractionRing