Vector bundles on p-adic curves and parallel transport
Algebraic Geometry
2007-05-23 v2 Number Theory
Abstract
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.
Cite
@article{arxiv.math/0403516,
title = {Vector bundles on p-adic curves and parallel transport},
author = {Christopher Deninger and Annette Werner},
journal= {arXiv preprint arXiv:math/0403516},
year = {2007}
}
Comments
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 pages