Theorems · Definition · commutative algebra

Algebra.SubmersivePresentation.sectionCotangent

{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.CotangentSpace →ₗ[S] P.toExtension.Cotangent

If P is a submersive presentation, this is the section of the map I ⧸ I ^ 2 → ⊕ S dxᵢ given by projecting to the summands indexed by σ and composing with the inverse of P.cotangentEquiv. By SubmersivePresentation.sectionCotangent_comp this is indeed a section.

Defined in

Mathlib.RingTheory.Smooth.StandardSmoothCotangent

Cited by

3 results in Mathlib

Foundations

Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFinite