[GS_M_AG] Semiorthogonal decompositions for stacks
ABSTRACT
I will explain a joint work in progress with Tudor Pădurariu and Yukinobu Toda on a construction of semiorthogonal decompositions on derived categories of coherent sheaves on algebraic stacks. This can be seen as a categorification of Donaldson–Thomas theory, and in particular, of a decomposition theorem in cohomology obtained in an earlier joint work. I will also mention its applications to categorification of quantum groups and to the Dolbeault geometric Langlands conjecture.
