Categories derivees et varietes de Deligne-Lusztig

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We prove a conjecture of Broue about the Jordan decomposition of blocks of finite reductive groups. We show that a block of a finite connected reductive group, in non-describing characteristic, is Morita-equivalent to a quasi-isolated block of a Levi subgroup. This involves showing that some local system over a Deligne-Lusztig variety has its mod l cohomology concentrated in one degree. We reduce this question to a question about tamely ramified local systems by proving that the category of perfect complexes for the group is generated by the images of the Deligne-Lusztig functors. Then, we describe the ramification at infinity of local systems associated to characters of tori.
54 pages, French

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Representation Theory, 20G40

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http://salesiana.dossiersoluciones.com/handle/123456789/63128

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0201146
 http://arxiv.org/abs/math/0201146

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arXiv