Cohomology of Deligne-Lusztig varieties and the fundamental group of the Drinfeld halfspace over a finite field.

在我最年轻的论文之一，我介绍了一个归纳的方法来确定的L-进上同调的Deligne-Lusztig品种的情况下，一般的线性群。该项目的第一部分的目的是适应的证明和技术的情况下，任意经典还原群。在另一个项目中，我们想确定有限域上的Drinfeld半空间的基本群。这完成了一个早期的项目，知道这些类型的不变量的其他周期域上的有限域。

In one of my youngest papers I introduce an inductive approach for determining the l-adic cohomology of Deligne-Lusztig varieties in the situation of the general linear group. The aim of the first part of the project is the adaption of the proofs and techniques to the case of arbitrary classical reductive groups. In the other project we want to determine the fundamental group of the Drinfeld halfspaceover a finite field. This completes an earlier project to know these kind of invariants for other period domains over finite fields.