Compositio Mathematica

Sur quelques représentations modulaires et p-adiques de GL2(Qp): I

((On Some Modular Representations and p-adics of)

Christophe Breuil a1
a1 CNRS et IHES 35, route de Chartres, 91440 Bures-sur-Yvette, France. e-mail:

Article author query
breuil c   [Google Scholar] 


Let p be a prime number and F a complete local field with residue field of characteristic p. In 1993, Barthel and Livné proved the existence of a new kind of $\overline{\bf F}_{p}$-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 $\overline{\bf F}_{p}$-representations of ${\rm Gal}(\overline{\bf Q}_{p}/{\bf Q}_{p})$.

Key Words: supersingular representations; intertwinings.