On capitulation of logarithmic classes

TL;DR

This paper develops a logarithmic analogue of a classical theorem on ideal class principalization in Hilbert class-fields, using group theory to describe transfer maps on logarithmic class groups.

Contribution

It introduces a logarithmic version of the Artin-Furw{"a}ngler theorem, expanding the understanding of class group principalization via group-theoretic methods.

Findings

Established a logarithmic principalization theorem

Applied group-theoretic description to logarithmic class groups

Extended classical results to a new logarithmic setting

Abstract

We establish a logarithmic version of the classical result of Artin-Furw{\"a}ngler on the principalization ofideal classes in the Hilbert class-field by applying the group theoretic description of the transfert map to logarithmic class-groups of degree 0.