Categories derivees et varietes de Deligne-Lusztig

Details Categories derivees et varietes de Deligne-Lusztig Categories derivees et varietes de Deligne-Lusztig

2002-01-16

arxiv.org/abs/math/0201146v1

Mathematics

Representation Theory

54 pages, French

Scientific paper

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.

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