Singularity Categories of Locally Bounded Categories with Radical Square Zero

2019/01/15 by Ales M. Bouhada, Bouhada, Ales M.
Mathematics · #math.CT #math.RT

paper · pdf · doi:10.48550/arxiv.1901.05087

Abstract

We study several singularity categories associated with a locally bounded \kk-linear category \C whose radical has square zero. Building on the work of Bautista and Liu \citeBL2017, we give explicit descriptions of \Dsg^b(\C), \Dsg^b(\C^\op), \Dsg^-(\proj-\C), \Dsg⁺(\inj-\C) as orbit categories of bounded derived categories of suitable semisimple abelian categories of quiver representations. We conclude with examples illustrating how generators of \Dsg^b(\C) can be read directly from the quiver of \C.

Related

• The derived category of an algebra with radical square zero
• The bounded derived categories of an algebra with radical squared zero
• The singularity category of an algebra with radical square zero
• Derived categories for algebras with radical square zero
• Relative singularity categories II: DG models