Theorems · Theorem · commutative algebra

Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange

∀ {R : Type u₁} {S : Type u₂} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {T : Type u₃}
  [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [inst_6 : IsScalarTower R S T] {ι : Type w₁}
  {σ : Type w₂} (Q : Algebra.Generators S T ι) (P : Algebra.Generators R S σ),
  LinearMap.liftBaseChange T (Algebra.Extension.CotangentSpace.map (Q.toComp P).toExtensionHom) ∘ₗ
      LinearMap.baseChange T P.toExtension.cotangentComplex =
    (Q.comp P).toExtension.cotangentComplex ∘ₗ
      LinearMap.liftBaseChange T (Algebra.Extension.Cotangent.map (Q.toComp P).toExtensionHom)

Defined in

Mathlib.RingTheory.Kaehler.JacobiZariski

Cited by

4 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower