Algebraický seminář

Chris Parker (Univ. Bielefeld): Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories

Abstract:  We will talk about recent joint work on a triangulated categorical generalisation of Neeman's theorem on the existence of bounded t-structures on the derived category of perfect complexes, which solved a bold conjecture by Antieau, Gepner, and Heller. In particular, under mild conditions, we show how the existence of a bounded t-structure on the compact objects of a triangulated category T implies that the singularity category of T vanishes. To achieve this, we show that certain t-structures can be lifted from a triangulated category to its completion, as well as introduce the notion of finitistic dimension for triangulated categories. This work is joint with Rudradip Biswas, Kabeer Manali Rahul, Hongxing Chen, and Junhua Zheng.