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


Author: Olivier Dudas
Journal: Represent. Theory 17 (2013), 647-662
MSC (2010): Primary 20C33
Published electronically: December 10, 2013
MathSciNet review: 3139556
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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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Additional Information

Olivier Dudas
Affiliation: Université Denis Diderot - Paris 7, UFR de Mathématiques, Institut de Mathématiques de Jussieu, Case 7012, 75205 Paris Cedex 13, France
Email: dudas@math.jussieu.fr

DOI: http://dx.doi.org/10.1090/S1088-4165-2013-00446-6
Received by editor(s): January 16, 2013
Received by editor(s) in revised form: July 10, 2013
Published electronically: December 10, 2013
Additional Notes: The author was supported by the EPSRC, Project No EP/H026568/1 and by Magdalen College, Oxford.
Article copyright: © Copyright 2013 American Mathematical Society