Circular annihilators of logarithmic classes

TL;DR

This paper introduces circular annihilators within logarithmic class groups of real abelian fields and proves they annihilate the logarithmic class group, leading to a proof of a logarithmic Solomon conjecture.

Contribution

It defines circular subgroups of logarithmic units and proves their annihilating property, providing a logarithmic analogue of Solomon's conjecture.

Findings

Circular subgroups of logarithmic units are defined.

These subgroups annihilate the logarithmic class group.

A proof of the logarithmic Solomon conjecture is established.

Abstract

Given a real abelian field F with group G and an odd prime number {\ell}, we define the circular subgroup of the pro-{\ell}-group of logarithmic units and we show that for any Galois morphism $\rho$ from the pro-{\ell}-group of logarithmic units to Z{\ell} [G ], the image of the circular subgroup annihilates the {\ell}-group of logarithmic classes. We deduce from this a proof of a logarithmic version of Solomon conjecture.