Cohomology of Deligne-Lusztig varieties for groups of type A

Details Cohomology of Deligne-Lusztig varieties for groups of type A Cohomology of Deligne-Lusztig varieties for groups of type A

2011-12-22

arxiv.org/abs/1112.5383v1

Mathematics

Representation Theory

Scientific paper

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_\ell, together with Craven's formula, holds for any unipotent
block whenever it holds for the principal Phi_1-block, that is for the variety
X(\pi).

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