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