Theorems · Definition · commutative algebra

Algebra.Extension.h1CotangentExtendScalarsEquiv

{R : Type u} →
  {S : Type v} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          (P : Algebra.Extension R S) → P.extendScalars.H1Cotangent ≃ₗ[S] Algebra.H1Cotangent P.Ring S

The first homology of the naive cotangent complex of P.extendScalars is linearly equivalent to that of S over P.Ring.

Defined in

Mathlib.RingTheory.Extension.ExtendScalars

Cited by

3 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra