| Résume | Let G be a split reductive group over a p-adic field F. We construct a natural coherent sheaf on the moduli stack of unipotent Langlands paramters for G, called the coherent Springer sheaf, whose self-Ext algebra is naturally isomorphic to the Iwahori Hecke algebra for G. As a consequence we deduce the existence of a fully faithful embedding of the Iwahori block of Rep(G) into the derived category of ind-coherent sheaves on the moduli stack of Langlands parameters. For G = GL_n we can go further and construct a fully faithful embedding of the category of all smooth representations of G into this derived category. |
