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Journal of the London Mathematical Society Advance Access published online on August 27, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm038
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© 2007 London Mathematical Society

Some remarks on the derived categories of coherent sheaves on homogeneous spaces

A. Samokhin

Département de Mathématiques
Université Paris 13
LAGA
avenue Jean-Baptiste Clément
93430 Villetaneuse
France
sasha{at}math.univ-paris13.fr
Current address:
Institute for Information Transmission Problems
B. Karetnyj per., 19
127994 Moscow
Russia

In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. We then show that the derived categories of coherent sheaves on flag varieties of classical type are generated by complete exceptional collections. Finally, we find complete exceptional collections in the derived categories of some homogeneous spaces of the symplectic groups of small rank.

samohin{at}mccme.ru

2000 Mathematics Subject Classification 18E30 (primary), 14M15 (secondary).

This work was supported in part by a French Government fellowship and the RFBR grant 07-01-00051.

Received November 23, 2005; revised September 18, 2006;
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