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On the derived category of Grassmannians in arbitrary characteristic

Part of:Rings and algebras arising under various constructionsSpecial varieties(Co)homology theoryBasic linear algebra

Published online by Cambridge University Press:  15 April 2015

Ragnar-Olaf Buchweitz,
Graham J. Leuschke and
Michel Van den Bergh
Ragnar-Olaf Buchweitz
Affiliation:
Department of Computer and Mathematical Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada email ragnar@utsc.utoronto.ca
Graham J. Leuschke
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA email gjleusch@math.syr.edu
Michel Van den Bergh
Affiliation:
Departement WNI, Universiteit Hasselt, 3590 Diepenbeek, Belgium email michel.vandenbergh@uhasselt.be
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Abstract

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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.

Keywords

Grassmannian varietyexceptional collectiontilting bundlesemi-orthogonal decompositionquasi-hereditary algebra

MSC classification

Primary:14F05: Sheaves, derived categories of sheaves and related constructions14M15: Grassmannians, Schubert varieties, flag manifolds
Secondary:16S38: Rings arising from non-commutative algebraic geometry15A75: Exterior algebra, Grassmann algebras

Information

Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 7 , July 2015, pp. 1242 - 1264
Copyright
© The Authors 2015 

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