| Speaker: | Tanmay Deshpande (Kavli IPMU) |
|---|---|
| Title: | Etale cohomology, l-adic sheaves and Deligne-Lusztig theory |
| Date (JST): | Thu, Dec 05, 2013, 13:40 - 18:00 |
| Place: | Seminar Room B |
| Abstract: | In the first part of my talk I will give a brief introduction to the theory of etale cohomology and the bounded derived category of l-adic complexes on a scheme. The main goal of the talk is to use this geometric theory to study the representation theory of finite groups of Lie type i.e. groups of the form G(F_q) where G is a reductive group defined over a finite field F_q. I will define certain varieties, known as Deligne-Lusztig varieties which are equipped with an action of the finite group G(F_q). Thus we get an induced action of G(F_q) on the l-adic cohomology of these Deligne-Lusztig varieties. Deligne and Lusztig proved that all irreducible representations of G(F_q) occur in the cohomology of the various Deligne-Lusztig varieties. Using this theory it is possible to partition the irreducible representations of G(F_q) into equivalence classes which are parametrized by semisimple conjugacy classes in the dual reductive group. I will try to illustrate these ideas explicitly for G=SL_2. |
| Remarks: | 1st 13:40 - 15:00, 2nd 15:30 - 18:00 |
