On the derived category of Grassmannians in arbitrary characteristic

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

Research output: Research - peer-reviewArticle

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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.

LanguageEnglish (US)
Pages1242-1264
Number of pages23
JournalCompositio Mathematica
Volume151
Issue number7
DOIs
StatePublished - Jul 25 2015

Fingerprint

Derived Category
Tilting
Grassmannian
Bundle
Arbitrary
Simple Module
Endomorphism Ring
Projective Module
Zero
Standards

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On the derived category of Grassmannians in arbitrary characteristic. / Buchweitz, Ragnar Olaf; Leuschke, Graham J.; Van Den Bergh, Michel.

In: Compositio Mathematica, Vol. 151, No. 7, 25.07.2015, p. 1242-1264.

Research output: Research - peer-reviewArticle

Buchweitz RO, Leuschke GJ, Van Den Bergh M. On the derived category of Grassmannians in arbitrary characteristic. Compositio Mathematica. 2015 Jul 25;151(7):1242-1264. Available from, DOI: 10.1112/S0010437X14008070
Buchweitz, Ragnar Olaf ; Leuschke, Graham J. ; Van Den Bergh, Michel. / On the derived category of Grassmannians in arbitrary characteristic. In: Compositio Mathematica. 2015 ; Vol. 151, No. 7. pp. 1242-1264
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