Principalization of logarithmic class groups

TL;DR

This paper extends previous results on abelian principalization from ray class groups to logarithmic class groups of number fields, broadening the understanding of their algebraic structure.

Contribution

It introduces a generalization of principalization results to logarithmic class groups, expanding the scope of prior work on tame ray class groups.

Findings

Established principalization results for logarithmic class groups.

Connected logarithmic class groups with classical ray class groups.

Provided new tools for studying algebraic properties of number fields.

Abstract

We extend to logarithmic class groups the results on abelian principalization of tame ray class groups of a number field obtained in a previous article.