Supersingular representations of GL_2(Q_p) and (phi,Gamma)-modules

Abstract

The purpose of this note is to give a direct proof of the fact that if one applies Colmez' functor to a two dimensional irreducible F_p^bar-representation of Gal(Q_p^bar/Q_p), one gets the restriction to the Borel subgroup of GL_2(Q_p) of a supersingular representation.