Classes logarithmiques et capitulation

TL;DR

This paper explores a logarithmic analogue of a classical number theory result, using group theory to analyze ideal class principalization in logarithmic class groups within Hilbert class fields.

Contribution

It introduces a logarithmic version of the Artin-Furw{"a}ngler theorem, applying group-theoretic methods to logarithmic class groups for principalization.

Findings

Logarithmic class groups are studied using group theory.

A logarithmic analogue of the Artin-Furw{"a}ngler result is established.

Principalization in Hilbert class fields is characterized logarithmically.

Abstract

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