On sections of arithmetic fundamental groups of open p-adic annuli

TL;DR

This paper proves that for small p-adic annuli, there are no sections of their arithmetic fundamental groups, which also implies the absence of such sections for the boundaries of p-adic curves.

Contribution

It establishes the non-existence of sections of arithmetic fundamental groups for certain p-adic geometric structures, extending understanding of their fundamental group properties.

Findings

No sections exist for small-radius p-adic annuli

Non-existence of sections for formal boundaries of p-adic curve germs

Results impact the understanding of p-adic fundamental groups

Abstract

We show the non-existence of sections of arithmetic fundamental groups of open p-adic annuli of small radii, this implies the non-existence of sections of arithmetic fundamental groups of formal boundaries of formal germs of p-adic curves.