English

A localisation theorem for singularity categories of proper dg algebras

Representation Theory 2023-07-06 v2

Abstract

Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of their singularity categories. This allows us to recover and generalise some known results on singularity categories of finite-dimensional algebras.

Keywords

Cite

@article{arxiv.2302.05054,
  title  = {A localisation theorem for singularity categories of proper dg algebras},
  author = {Haibo Jin and Dong Yang and Guodong Zhou},
  journal= {arXiv preprint arXiv:2302.05054},
  year   = {2023}
}

Comments

Section 3 is new, and in Section 4 the base ring is changed from a field to a commutative noetherian ring and in Section 6 the base ring is changed from a field to an arbitrary commutative ring