Sur quelques représentations modulaires et p-adiques de GL2(Qp): I: (On Some Modular Representations and p-adics of

Abstract

Let p be a prime number and F a complete local field with residue field of characteristic p. In 1993, Barthel and Livne proved the existence of a new kind of \({\bar F_p }\)-representations of GL2(F) that they called 'supersingular' and on which one knows almost nothing. In this article, we determine all the supersingular representations of GL2(Qp) with their intertwinings. This classification shows a natural bijection between the set of isomorphism classes of supersingular representations of GL2(Qp) and the set of isomorphism classes of two-dimensional irreducible \({\bar F_p }\)-representations of \({Gal}\left( {{\bar Q}_p /{Q}_p } \right)\).