Tuesday, December 06, 14:00

Xiaofa Chen (Paris IMJ), Derived equivalences and liftable functors.

Abstract:
It is a well-known open question whether a triangle equivalence between derived categories of finite-dimensional algebras is necessarily standard, namely isomorphic to a derived tensor functor by a two-sided tilting complex. In this talk, we propose to attack this problem from the viewpoint of dg category theory. We give a proof of the following folklore result: when a finite-dimensional algebra A is derived equivalent to a smooth projective scheme, any derived equivalence between A and another finite-dimensional algebra B is necessarily standard. The ingredients of the proof seem to be of independent interest. This is a joint work with Xiao-Wu Chen.