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On the derived category of Grassmannians in arbitrary characteristic

Published online by Cambridge University Press:  15 April 2015

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.

Type
Research Article
Copyright
© The Authors 2015 

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