Homogeneous p-adic vector bundles on abelian varieties that are analytic tori

We are investigating homogeneous p-adic vector bundles on abelian varieties that are analytic tori. We show that for each homogeneous vector bundle on such a variety there exists an integer N > 0, such that the pullback of this vector bundle via the N-multiplication is attached to an integral representation of the topological fundamental group. Received: 8 July 2008