Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Friday, October 13, 2017 - 14:15 in T2-213

T-structures on the derived categories of coherent sheaves on flag varieties and the Frobenius morphism

A talk in the 'Seminar Representation Theory of Algebras' series by
Alexander Samokhin from Düsseldorf
Abstract: We will talk about semiorthogonal decompositions of the derived categories of coherent sheaves on flag varieties that are compatible with the action of Frobenius morphism on coherent sheaves via push-forward and pull-back functors. We start with an example of such a decomposition, and, in particular, show how it implies Kempf's vanishing theorem. In some cases, refinements of that decomposition define, via derived Morita equivalence, the non-standard t-structures on the derived categories of flag varieties. These t-structures and their duals are related to each other via an autoequivalence of the ambient derived category whose square is isomorphic to the Serre functor. We will treat in detail the case of the groups of rank two.