Appears in collection : A conference in honor of Arthur Ogus on the occasion of his 70th birthday

Let X be a smooth connected algebraic variety over a p-adic field k and let L be a Q_p étale local system on X. I will show that if the stalk of L at one point of X, regarded as a p-adic Galois representation, is de Rham, then the stalk of L at every point of X is de Rham. This is a joint work with Ruochuan Liu.