Footnote:
Druckausg. u.d.T.: P-adic vector bundles on curves and abelian varieties and representations of the fundamental group
Description:
We examine and compare different approaches to p-adic integration and the p-adic Riemann-Hilbert-correspondence. We compare the parallel transport of C. Deninger and A. Werner with the parallel-transport of Y. Andre and V. Berkovich on curves. In a special case we show that these constructions are compatible with G. Faltings' p-adic Simpson-correspondence. For abelian varieties with good ordinary reduction, we examine a construction of C. Deninger and A. Werner and show, that there is an equivalence of categories between the category of temperate representation of the Tate-module and the category of translation invariant vector bundles, that are equipped with canonical p-adic connections. On Tate-elliptic curves we relate G. Faltings' Phi-bounded representations to temperate representations, this generalizes a result of G. Herz.