On the derived category of Grassmannians in arbitrary characteristic

Ragnar-Olaf Buchweitz, Graham J. Leuschke, Michel Van den Bergh

Published 2010-06-08, updated 2013-11-02Version 5

In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's well-known characteristic-zero results we construct dual exceptional collections on them (which are however not strong) as well as a tilting bundle. We show that this tilting bundle has a quasi-hereditary endomorphism ring and we identify the standard, costandard, projective and simple modules of the latter.