Deligne-Lusztig varieties

Abstract

In this thesis we expose some of the theory behind Deligne-Lusztig varieties. To this end, we develop the general theory of flag varieties, the theory of BN-pairs, and the theory of varieties defined over finite ground fields. With these tools in hand, we define Deligne-Lusztig varieties. We then study the Deligne-Lusztig varieties associated with general linear groups using flags, and give a complete description in the case of GL3.