ALGB Seminar: Sondre Kvamme (Université Paris Sud)

Title: The singularity category in Iyama's higher Auslander-Reiten theory

Abstract: The singularity category of a noetherian ring was first studied by Buchweitz as a useful invariant of the ring. It is a triangulated category which can for example detect if the global dimension of the ring is finite. The goal of this talk is to explain a link between Iyama's higher Auslander- Reiten theory and the singularity category. More precisely, for an exact category having enough projectives and with a dZ-cluster tilting subcategory, we show that the singularity category has a dZ-cluster tilting subcategory.  We will start with a short introduction to higher Auslander-Reiten theory, before we go on to state this main result. If time permits, we will also talk a bit about the proof, which uses the description of the singularity category as the stabilization of a right triangulated category due to Keller and Vossieck.