Coxeter orbits and Brauer trees
نویسنده
چکیده
We study the cohomology with modular coefficients of Deligne-Lusztig varieties associated to Coxeter elements. Under some torsion-free assumption on the cohomology we derive several results on the principal l-block of a finite reductive group G(Fq) when the order of q modulo l is assumed to be the Coxeter number. These results include the determination of the planar embedded Brauer tree of the block (as conjectured by Hiss, Lübeck and Malle in [25]) and the derived equivalence predicted by the geometric version of Broué’s conjecture [7].
منابع مشابه
Coxeter orbits and Brauer trees II
The purpose of this paper is to discuss the validity of the assumptions (W) and (S) stated in [12], about the torsion in the modular l-adic cohomology of Deligne-Lusztig varieties associated with Coxeter elements. We prove that both (W) and (S) hold except for groups of type E7 or E8.
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تاریخ انتشار 2017