Vector bundles on p-adic curves and parallel transport II

TL;DR

This paper extends the theory of etale parallel transport to a broader class of vector bundles on p-adic curves, including those stable under ramified pullbacks, and constructs related p-adic representations.

Contribution

It introduces an extended framework for parallel transport on slope zero vector bundles and constructs p-adic representations for non-zero slope bundles on p-adic curves.

Findings

Extended parallel transport theory to more vector bundles.

Constructed p-adic representations for non-zero slope bundles.

Demonstrated stability under ramified pullbacks.

Abstract

We extend our previous theory of etale parallel transport to a larger class of slope zero vector bundles on p-adic curves. The new class is stable under pullback by ramified coverings. We also construct p-adic representations of a central extension of the fundamental group for certain bundles of non-zero slope.