Cohomology of Deligne-Lusztig varieties for unipotent blocks of 𝐺𝐿_{𝑛}(𝑞)

Dudas, Olivier

doi:10.1090/S1088-4165-2013-00446-6

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

Represent. Theory 17 (2013), 647-662

DOI: https://doi.org/10.1090/S1088-4165-2013-00446-6

Published electronically: December 10, 2013

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Abstract:

We study the cohomology of parabolic Deligne-Lusztig varieties associated to unipotent blocks of $\mathrm {GL}_n(q)$. We show that the geometric version of Broué’s conjecture over $\overline {\mathbb {Q}}_\ell$, together with Craven’s formula, holds for any unipotent block whenever it holds for the principal $\Phi _1$-block.

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