On the derived category of the Iwahori-Hecke algebra

Hellmann, Eugen

Abstract

We state a conjecture that relates the derived category of smooth representations of a p-adic split reductive group with the derived category of (quasi-)coherent sheaves on a stack of L-parameters. We investigate the conjecture in the case of the principal block of GLn by showing that the functor should be given by the derived tensor product with the family of representa- tions interpolating the modified Langlands correspondence over the stack of L-parameters that is suggested by the work of Helm and Emerton-Helm.