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

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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.