On the derived category of Grassmannians in arbitrary characteristic

TL;DR

This paper extends Kapranov's results to Grassmannians over arbitrary characteristic, constructing dual exceptional collections and a tilting bundle with a quasi-hereditary endomorphism ring.

Contribution

It generalizes the construction of exceptional collections and tilting bundles on Grassmannians to arbitrary characteristic, identifying their algebraic structures.

Findings

Constructed dual exceptional collections in arbitrary characteristic

Established the tilting bundle has a quasi-hereditary endomorphism ring

Identified standard, costandard, projective, and simple modules

Abstract

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.