Download Paper (published version of 2015-07-22)
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.
This is a complete revision of the original note, now four times as long with a lot of new material. Rather than folding it into part 2 of the determinantal varieties paper, we decided to publish it on its own.