Séance Séminaire

Séminaire de Théorie des Nombres de Montpellier

Towards a Langlands correspondence for Hecke modules of SL(n) in characteristic p

In this talk, we show how to realize the pro-p-Iwahori-Hecke algebra of SL_n as a subalgebra of the pro-p-Iwahori-Hecke algebra of GL(n). Using the interplay between these two algebras, we deduce two main results: one on a numerical Langlands correspondence between "packets" of Hecke modules and mod-p projective Galois representations, and another on an equivalence of categories between Hecke modules and mod-p representations of SL_n.