Theorems · Theorem · commutative algebra

Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor_aux

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] {G : Type u}
  [inst_3 : Group G] [inst_4 : MulSemiringAction G B] [inst_5 : SMulCommClass G A B] [inst_6 : TopologicalSpace G]
  (Q : Ideal B) {N N' : OpenNormalSubgroup G} (e : N ≤ N'),
  ∀ x ∈ MulAction.stabilizer (G ⧸ ↑N.toOpenSubgroup) (Ideal.under (↥(FixedPoints.subalgebra A B ↥↑N.toOpenSubgroup)) Q),
    (QuotientGroup.map (↑N.toOpenSubgroup) N'.toOpenSubgroup.1 (MonoidHom.id G) e) x ∈
      MulAction.stabilizer (G ⧸ ↑N'.toOpenSubgroup) (Ideal.under (↥(FixedPoints.subalgebra A B ↥↑N'.toOpenSubgroup)) Q)

Defined in

Mathlib.RingTheory.Invariant.Profinite

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraGroupMulSemiringActionSMulCommClassTopologicalSpace