A non-abelian Stickelberger theorem

TL;DR

This paper develops a non-abelian generalization of the Stickelberger theorem, constructing elements in group rings that annihilate parts of class groups in Galois extensions using Artin L-functions.

Contribution

It introduces a non-abelian version of the Stickelberger element, extending classical results to broader Galois groups and connecting L-functions with class group annihilation.

Findings

Constructed elements in Z_(p)[G] that annihilate the p-part of class groups.

Extended classical Stickelberger theory to non-abelian Galois extensions.

Provided conditions under which the construction applies.

Abstract

Let L/k be a finite Galois extension of number fields with Galois group G. For every odd prime p satisfying certain mild technical hypotheses, we use values of Artin L-functions to construct an element in the centre of the group ring Z_(p)[G] that annihilates the p-part of the class group of L.