p-adic representations and vector bundles on Mumford curves

Christopher Deninger andAnnette Werner constructed a functor that associates representations of the algebraic fundamental group of an algebraic curve to a class of vector bundles on that curve. We compare this to a construction byFaltings for Mumford curves that associates representations of the Schottky group to semistable vector bundles of degree 0. We prove that for a certain class of vector bundles on Mumford curves the constructions induce isomorphic representations.