Tuesday, December 06, 14:00
Xiaofa Chen (Paris IMJ), Derived equivalences and liftable functors.
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.