Theorems · Definition · commutative algebra

Algebra.Generators.basisCotangentAway

{R : Type u_1} →
  (S : Type u_2) →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          (r : R) →
            [inst_3 : IsLocalization.Away r S] →
              Module.Basis Unit S (Algebra.Generators.localizationAway S r).toExtension.Cotangent

The basis of (g * X - 1) / (g * X - 1)² given by the image of g * X - 1. This is def-eq to (SubmersivePresentation.localizationAway T g).basisCotangent, but `` (SubmersivePresentation.localizationAway T g).toExtension = (Generators.localizationAway T g).toExtension ` is not reducibly def-eq. Hence using the general SubmersivePresentation.basisCotangent leads to erw` hell.

Defined in

Mathlib.RingTheory.Smooth.StandardSmoothCotangent

Cited by

3 results in Mathlib

Foundations

Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIsLocalization.Away