Theorems · Definition · commutative algebra

Algebra.tensorH1CotangentOfIsLocalization

(R : Type u_1) →
  {S : Type u_2} →
    (T : Type u_3) →
      [inst : CommRing R] →
        [inst_1 : CommRing S] →
          [inst_2 : CommRing T] →
            [inst_3 : Algebra R S] →
              [inst_4 : Algebra R T] →
                [inst_5 : Algebra S T] →
                  [IsScalarTower R S T] →
                    (M : Submonoid S) →
                      [IsLocalization M T] → TensorProduct S T (Algebra.H1Cotangent R S) ≃ₗ[T] Algebra.H1Cotangent R T

let p be a submonoid of an R-algebra S. Then Sₚ ⊗ H¹(L_{S/R}) ≃ H¹(L_{Sₚ/R}).

Defined in

Mathlib.RingTheory.Etale.Kaehler

Cited by

2 results in Mathlib

Foundations

Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTowerIsLocalization