Dionne, Christopher2013-11-072013-11-0720092009Source: Masters Abstracts International, Volume: 48-05, page: 3020.http://hdl.handle.net/10393/28351http://dx.doi.org/10.20381/ruor-12509In 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 GL3.70 p.enMathematics.Thesis