We define functorial isomorphisms of parallel transport along etale paths for
a class of vector bundles on a p-adic curve. All bundles of degree zero whose
reduction is strongly semistable belong to this class. In particular, they give
rise to representations of the algebraic fundamental group of the curve. This
may be viewed as a partial analogue of the classical Narasimhan-Seshadri theory
of vector bundles on compact Riemann surfaces.Comment: The main result is now valid for arbitrary reduction; Theorems 5, 16,
17, 18 and 20 are either improvements of results in the first version or new.
The article will appear in Annales Sci. de l'ENS 56 page
