Abstract:

Let G be a simple algebraic group with Borel subgroup B. The Borel-Weil-Bott theorem describes the vanishing behavior and the structure of the right derived functors of induction from B to G at simple B-modules, if the underlying field is of characteristic 0. In this talk, I will present a simple proof of the Borel-Weil-Bott theorem via derived categories and (total) derived functors. The proof also allows us to obtain some new insights into the vanishing behavior and the structure of the right derived functors of induction from B to G over fields of positive characteristic.