Monodromy Groups of Vector Bundles on p-adic Curves

TL;DR

This paper explores the monodromy groups associated with vector bundles on p-adic curves, focusing on their images, Zariski closures, and Tannaka dual groups within a p-adic analogue of the Narasimhan-Seshadri correspondence.

Contribution

It investigates the structure and properties of monodromy groups in the p-adic setting, extending the classical correspondence to new algebraic contexts.

Findings

Characterization of monodromy group images

Analysis of Zariski closures of these groups

Identification of Tannaka dual groups in the p-adic framework

Abstract

In [DW05] and [DW07], C. Deninger and A. Werner developed a partial p-adic analogue of the classical Narasimhan-Seshadri correspondence between vector bundles and representations of the fundamental group. We will investigate the various monodromy groups that occur in this theory, that is the image of these representations and their Zariski closure as well as the Tannaka dual group of these vector bundles.