Cohomology of Deligne-Lusztig varieties for groups of type A
Abstract
We study the cohomology of parabolic Deligne-Lusztig varieties associated to unipotent blocks of GLn(q). We show that the geometric version of Brou\'e's conjecture over Q, together with Craven's formula, holds for any unipotent block whenever it holds for the principal Phi1-block, that is for the variety X(π).
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