Tuesday, July 07, 14:00, 7.527
Chrysostomos Psaroudakis (NTNU Trondheim)
The Realisation Functor and
Derived Equivalences for Abelian Categories.
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.