On the derived category of Grassmannians in arbitrary characteristic

Ragnar Olaf Buchweitz, Graham J. Leuschke, Michel Van Den Bergh

Research output: Contribution to journalArticle

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1242-1264
Number of pages23
JournalCompositio Mathematica
Volume151
Issue number7
DOIs
StatePublished - Jul 25 2015

Keywords

  • Grassmannian variety
  • exceptional collection
  • quasi-hereditary algebra
  • semi-orthogonal decomposition
  • tilting bundle

ASJC Scopus subject areas

  • Algebra and Number Theory

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