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On the derived category of Grassmannians in arbitrary characteristic

Part of: Special varieties Basic linear algebra (Co)homology theory Rings and algebras arising under various constructions

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 [email protected]
Graham J. Leuschke
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA email [email protected]
Michel Van den Bergh
Affiliation:
Departement WNI, Universiteit Hasselt, 3590 Diepenbeek, Belgium email [email protected]
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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 constructions 14M15: Grassmannians, Schubert varieties, flag manifolds
Secondary: 16S38: Rings arising from non-commutative algebraic geometry 15A75: Exterior algebra, Grassmann algebras
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 7 , July 2015 , pp. 1242 - 1264
Copyright
© The Authors 2015 

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