Abstract
In this article, we study the mod ℓ cohomology of some Deligne–Lusztig varieties for GLn(q). We prove that the cohomology groups of these varieties are torsion-free under some conditions on the characteristic. Under the torsion-free assumption we can compute the cohomology groups explicitly and we prove that the cohomology complex satisfies a partial-tilting condition, which is one of the necessary conditions in the geometric version of Broué's abelian defect group conjecture.
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