STNB2020(34th edition)

Delinge-Lusztig curves are diophantine stable

Joan-C. Lario

Abstract

In the mid 70s, Deligne-Lusztig varieties appeared on the scene to describe the character table of all finite simple groups of Lie type, the vast majority in the classification of finite simple groups. The achievement of Deligne and Lusztig entailed a second important application of $\ell$-adic cohomology, after the successful proof of the Weil conjectures. In this talk, we focus on the one dimensional case. Deligne-Lusztig curves enjoy remarkable properties and are useful, for instance, to Coding Theory. We shall observe that they are DS-curves (diophantine stable) and try to give reasons for it.