Theorems · Definition · commutative algebra

galRestrict

(A : Type u_1) →
  (K : Type u_2) →
    (L : Type u_3) →
      (B : Type u_6) →
        [inst : CommRing A] →
          [inst_1 : CommRing B] →
            [inst_2 : Algebra A B] →
              [inst_3 : Field K] →
                [inst_4 : Field L] →
                  [inst_5 : Algebra A K] →
                    [IsFractionRing A K] →
                      [inst_7 : Algebra K L] →
                        [inst_8 : Algebra A L] →
                          [IsScalarTower A K L] →
                            [inst_10 : Algebra B L] →
                              [IsScalarTower A B L] →
                                [IsIntegralClosure B A L] → [Algebra.IsAlgebraic K L] → Gal(L/K) ≃* B ≃ₐ[A] B

The restriction Aut(L/K) → Aut(B/A) in an AKLB setup.

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

13 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFieldFieldAlgebraIsFractionRingAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerIsIntegralClosureAlgebra.IsAlgebraic