Speaker:  Rudradip Biswas,  University of Warwick

Title - Bounded t-structures with completion theory

Abstract - I will report on a recent joint paper with Hongxing Chen, K Manali Rahul, Chris Parker and Junhua Zheng (arxiv:2401.00130). I will show that for triangulated categories satisfying a small finiteness condition, its own “singularity category”, which I will define in terms of its Neeman-completion, is a categorical obstruction to the existence of bounded t-structures. This, and related results, generalize all of the results of a recent Neeman paper (“Bounded t-structures on perfect complexes”, to appear in Acta Math) from derived categories of schemes (where his work settled an Antieau-Gepner-Heller conjecture) to general triangulated categories with different methods. I will focus on some applications of our treatment to the categories of perfects and almost-perfects in the setup of E1 rings.