English

Dg-separable dg-extensions

Rings and Algebras 2026-01-07 v2 Representation Theory

Abstract

We define and characterise completely dg-separable dg-extensions φ:(A,dA)(B,dB)\varphi:(A,d_A)\rightarrow (B,d_B). We completely characterise the case of graded commutative dg-division algebras in characteristic different from 22. We prove that for a dg-separable extension a short exact sequence of dg-modules over (B,dB)(B,d_B) splits if and only if the restriction to (A,dA)(A,d_A) splits.

Cite

@article{arxiv.2412.06526,
  title  = {Dg-separable dg-extensions},
  author = {Alexander Zimmermann},
  journal= {arXiv preprint arXiv:2412.06526},
  year   = {2026}
}
R2 v1 2026-06-28T20:27:56.596Z