Por Jorge Vitória (City, University of London).

Abstract: Both in algebra and in geometry, Grothendieck categories (e.g. quasicoherent sheaves over a scheme, modules over a ring, …) and their derived categories play a prominent role. In this talk we approach the problem of identifying when two Grothendieck categories have equivalent derived categories. We tackle this problem using a generalisation of classical tilting theory, as set up by Happel, Rickard and Keller in the late 1980s. Our target is two-fold: identify Grothendieck categories that are nicely embedded (as hearts of t-structures) in triangulated categories of interest, and determine whether (or when) that embedding naturally extends to a derived equivalence.

This is based on joint work with C. Psaroudakis and on joint work with L. Angeleri Hügel and F. Marks.