Theorems · Theorem · commutative algebra

Ideal.Quotient.stabilizerHom_surjective_of_profinite

∀ {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]
  [CompactSpace G] [TotallyDisconnectedSpace G] [IsTopologicalGroup G] [inst_10 : TopologicalSpace B]
  [DiscreteTopology B] [ContinuousSMul G B] (P : Ideal A) (Q : Ideal B) [Q.IsPrime] [inst_14 : Q.LiesOver P]
  [Algebra.IsInvariant A B G], Function.Surjective ⇑(Ideal.Quotient.stabilizerHom Q P G)

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

Defined in

Mathlib.RingTheory.Invariant.Profinite

Cited by

0 results in Mathlib

Foundations

Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraGroupMulSemiringActionSMulCommClassTopologicalSpaceCompactSpaceTotallyDisconnectedSpaceIsTopologicalGroupTopologicalSpaceDiscreteTopologyContinuousSMulIdeal.IsPrimeIdeal.LiesOverAlgebra.IsInvariant