Equations differentielles p-adiques et (phi,N)-modules filtres

The goal of this article is to show that the following two categories are equivalent (1) the category of filtered (phi,N,G_K)-modules (2) the category of (phi,Gamma_K)-modules over the Robba ring such that the Lie algebra of Gamma_K acts locally trivially. Furthermore, we show that under this equivalence, the admissible filtered (phi,N,G_K)-modules correspond to the etale (phi,Gamma_K)-modules, which gives a new proof of Colmez-Fontaine's theorem.