The canonical fractional Galois ideal at s=0

TL;DR

This paper investigates the canonical fractional Galois ideal at s=0, linking Stickelberger elements with Stark units and exploring their role in annihilator relations involving algebraic K-groups.

Contribution

It establishes a connection between the canonical Galois module associated with Stickelberger elements and Stark units in a specific case.

Findings

Proves a link between the Galois module and Stark units.

Provides evidence supporting conjectural annihilator relations.

Enhances understanding of Stickelberger elements in algebraic number theory.

Abstract

The Stickelberger elements attached to an abelian extension of number fields conjecturally participate, under certain conditions, in annihilator relations involving higher algebraic K-groups. In [Victor P. Snaith, Stark's conjecture and new Stickelberger phenomena, Canad. J. Math. 58 (2) (2006) 419--448], Snaith introduces canonical Galois modules hoped to appear in annihilator relations generalising and improving those involving Stickelberger elements. In this paper we study the first of these modules, corresponding to the classical Stickelberger element, and prove a connection with the Stark units in a special case.