Cohomology of Deligne-Lusztig varieties for unipotent blocks of $\mathrm {GL}_n(q)$

Olivier Dudas
2013 Representation Theory: An Electronic Journal of the AMS  
We study the cohomology of parabolic Deligne-Lusztig varieties associated to unipotent blocks of GL n (q). We show that the geometric version of Broué's conjecture over Q , together with Craven's formula, holds for any unipotent block whenever it holds for the principal Φ 1 -block.
doi:10.1090/s1088-4165-2013-00446-6 fatcat:gauhpsdepfhcja5wdjr7z4j5zy