Class field theory for open curves over local fields, II

TL;DR

This paper advances the understanding of class field theory for open curves over local fields of characteristic p, focusing on the reciprocity map and its kernel's p-part under ramification restrictions.

Contribution

It extends previous work by analyzing the p-part of the kernel of the reciprocity map for open curves with rank 0 over local fields of characteristic p.

Findings

Determined the p-part of the kernel of the reciprocity map for rank 0 open curves.

Analyzed the impact of ramification restrictions on the kernel.

Extended class field theory results to new cases of open curves.

Abstract

As a continuation of arXiv:1412.6888, we study the reciprocity map for an open curve $X$ over a local field of characteristic $p>0$. We determine the $p$-part of the kernel of the reciprocity map after restricting ramification when the rank of $X$ is $0$.