论文标题
mod $ \ ell $ $ \ operatatorName {gl} _n（q）$的某些deligne-lusztig品种
Mod $\ell$ cohomology of some Deligne-Lusztig varieties for $\operatorname{GL}_n(q)$
论文作者
论文摘要
在本文中，我们研究了某些Deligne-lusztig品种的Mod $ \ ell $共同体，用于$ \ operatatorName {gl} _n（q）$。我们证明，在某些情况下，这些品种的共同体组无扭转。在无扭转假设下，我们可以明确地计算同种学组，并证明协同学络合物满足了部分倾斜条件，这是Broué的Abelian Abelian缺陷组群体的几何版本中的必要条件之一。
In this article, we study the mod $\ell$ cohomology of some Deligne-Lusztig varieties for $\operatorname{GL}_n(q)$. 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 partial-tilting condition, which is one of the necessary conditions in the geometric version of Broué's abelian defect group conjecture.
