Tuesday, July 07, 14:00, 7.527

Chrysostomos Psaroudakis (NTNU Trondheim)
The Realisation Functor and Derived Equivalences for Abelian Categories.

Abstract:
In this talk we show how to obtain derived equivalences for abelian categories from not necessarily compact tilting and cotilting objects. The key ingredients of this result are the realisation functor of Beilinson-Bernstein-Deligne and a notion of (co)tilting objects in triangulated categories that we introduce. The first part of the talk is devoted to explaining the realisation functor. We then continue by discussing (not necessarily compact) (co)silting objects in appropriate triangulated categories and in the last part we present the main result. As a particular case we explain how derived equivalences between Grothendieck categories can be realised as cotilting equivalences. This is joint work with Jorge Vitoria.