Theorems · Definition · commutative algebra

Algebra.SubmersivePresentation.cotangentEquiv

{R : Type u_1} →
  {S : Type u_2} →
    {ι : Type u_3} →
      {σ : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Algebra R S] →
              [inst_3 : Finite σ] → (P : Algebra.SubmersivePresentation R S ι σ) → P.toExtension.Cotangent ≃ₗ[S] σ → S

The isomorphism of S-modules between I ⧸ I ^ 2 and σ → S given by P.relation i ↦ ∂ⱼ (P.relation i).

Defined in

Mathlib.RingTheory.Smooth.StandardSmoothCotangent

Cited by

3 results in Mathlib

Foundations

Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFinite