Theorems · Definition · commutative algebra

Algebra.SubmersivePresentation.basisKaehlerOfIsCompl

{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) →
                  {κ : Type u_5} →
                    {f : κ → ι} →
                      Function.Injective f → IsCompl (Set.range f) (Set.range P.map) → Module.Basis κ S Ω[S⁄R]

Given a submersive presentation of S as R-algebra, any indexing type κ complementary to the σ in ι indexes a basis of Ω[S⁄R]. See SubmersivePresentation.basisKaehler for the special case κ = (Set.range P.map)ᶜ.

Defined in

Mathlib.RingTheory.Smooth.StandardSmoothCotangent

Cited by

2 results in Mathlib

Foundations

Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFinite