Embedding problems for open subgroups of the fundamental group

TL;DR

This paper investigates embedding problems related to the fundamental group of a smooth affine curve over an algebraically closed field of positive characteristic, focusing on subgroups and their properties.

Contribution

It provides new insights into embedding problems for the fundamental group of affine curves and explores subgroup structures in positive characteristic.

Findings

Characterization of embedding problems for $\

Analysis of subgroup embeddings in $\

Results on the structure of $\

Abstract

Let $C$ be a smooth irreducible affine curve $C$ over an algebraically closed field of positive characteristic and let $\pi_1(C)$ be its fundamental group. We study various embedding problems for $\pi_1(C)$ and its subgroups.