Prinzipalbündel auf p-adischen Kurven und Paralleltransport

Abstract

We define functorial isomorphisms of parallel transport along etale paths for a class of G-principal bundles on a p-adic curve where G is a connected reductive algebraic group of finite presentation. This class consists of all principal bundles with potentially strongly semistable reduction of degree zero. In particular, this construction gives us a continous functor from the etale fundamental grupoid of the given curve to the category of topological spaces with a simply transitive continous right G(\mathbb{C}_{p})-action for every such principal bundle. This generalizes the construction of functorial isomorphisms of parallel tranport for a certain class of vector bundles on a p-adic curve by Deninger and Werner and it may be viewed as a partial p-adic analogue of the classical theory by Ramanathan of principal bundles on compact Riemann surfaces which again generalizes the classical Narasimham-Seshadri theory of vector bundles on compact Riemann surfaces.