Appears in collection : Franco-Asian Summer School on Arithmetic Geometry in Luminy / Ecole d'été franco-asiatique sur la géométrie arithmétique à Luminy

Let $p$ be a prime number. The classical work of Sen attaches an operator (called the Sen operator) to every finite-dimensional continuous $p$-adic representation of the absolute Galois group of $Q_{p}$. We will present a generalization of this construction to locally analytic Galois representations (which are possibly infinitedimensional and will be defined in the talk) and discuss several applications.