### Representations p-adiques et equations differentielles, by Laurent Berger

Abstract: In this paper, we associate to every $p$-adic representation $V$ a $p$-adic differential equation $\mathbf{D}^{\dagger}_{\mathrm{rig}}(V)$, that is to say a module with a connection over the Robba ring. We do this via the theory of Fontaine's $(\phi,\Gamma_K)$-modules. This construction enables us to relate the theory of $(\phi,\Gamma_K)$-modules to $p$-adic Hodge theory.

Laurent Berger <laurent@brandeis.edu>