RTG Seminar on Number Theory Seminar

A classical result of Borel and Bernstein shows that the category of smooth complex representations of a p-adic reductive group G which are generated by their Iwahori-invariant vectors is equivalent to the category of modules over an Iwahori-Hecke algebra H. This makes the algebra H an extremely useful tool in studying the representation theory of G, and thus in the Local Langlands Program. When the field of complex numbers is replaced by a field of characteristic p, this equivalence no longer holds; however, one can recover an equivalence by passing to derived categories and upgrading H to a certain differential graded algebra. I'll explain these results, and discuss some concrete computational problems. Speaker(s): Karol Koziol (UM)