Special Year Workshop on p-adic Arithmetic Geometry

Let $E$ be a finite degree extension of $Qp$. Given a mod p representation of the absolute Galois group of E we construct a sheaf on a punctured absolute Banach-Colmez space that should give the first step in the construction of the mod p local Langlands correspondence as a representation of the mirabolic subgroup of $GL2(E)$. We will explain the construction of this sheaf, its conjectural properties and the link with the recent work of Breuil, Herzig, Hu Morra, and Schraen about local-global compatibility.