| Résume | 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 $SL_n$. |
