Local and global structure of connections on nonarchimedean curves

TL;DR

This paper refines the understanding of vector bundles with connections on p-adic analytic curves, focusing on their structure and the convergence of local horizontal sections, advancing the theoretical framework in non-archimedean geometry.

Contribution

It provides improved results and refinements on the structure and convergence properties of connections on non-archimedean curves, building on prior foundational work.

Findings

Enhanced structural descriptions of connections on p-adic curves

Refined criteria for convergence of local horizontal sections

Integration of recent improvements in non-archimedean geometry

Abstract

Consider a vector bundle with connection on a p-adic analytic curve in the sense of Berkovich. We collect some improvements and refinements of recent results on the structure of such connections, and on the convergence of local horizontal sections. This builds on work from the author's 2010 book and on subsequent improvements by Baldassarri and Poineau-Pulita.