Theorems · Definition · commutative algebra

Algebra.Extension.tensorCotangentOfFlat

{R : Type u_1} →
  {S : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          (P : Algebra.Extension R S) →
            (T : Type u_3) →
              [inst_3 : CommRing T] →
                [inst_4 : Algebra R T] → [Module.Flat R T] → TensorProduct R T P.Cotangent ≃ₗ[T] P.baseChange.Cotangent

If T is flat over R, there is a T-linear isomorphism T ⊗[R] P.Cotangent ≃ₗ[T] (P.baseChange).Cotangent.

Defined in

Mathlib.RingTheory.Extension.Cotangent.BaseChange

Cited by

3 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraModule.Flat