Conjectures of Brumer, Gross and Stark

TL;DR

This paper introduces generalizations of conjectures related to number field class groups, connecting them to broader conjectures in algebraic number theory and Iwasawa theory, highlighting their interrelations.

Contribution

It provides an overview of conjectures extending Brumer and Stark's work, relating them to the equivariant Tamagawa number conjecture and Iwasawa theory.

Findings

Connections between conjectures clarified

Implications for class group annihilators discussed

Relations to p-adic L-functions explored

Abstract

We give an introduction to generalisations of conjectures of Brumer and Stark on the annihilator of the class group of a number field. We review the relation to the equivariant Tamagawa number conjecture, the main conjecture of Iwasawa theory for totally real fields, and a conjecture of Gross on the behaviour of $p$-adic Artin $L$-functions at zero.