On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture

TL;DR

This paper demonstrates that for odd primes, the non-abelian Brumer and Brumer-Stark conjectures' p-primary parts follow from the equivariant Iwasawa main conjecture for totally real fields, independent of the mu-invariant.

Contribution

It establishes a link between the non-abelian Brumer-Stark conjectures and the EIMC without assuming mu-invariant vanishing, enabling new unconditional proofs.

Findings

Proves the implications of the EIMC for the non-abelian Brumer-Stark conjectures.

Provides unconditional proofs in many new cases.

Shows independence from the mu-invariant vanishing assumption.

Abstract

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant. In combination with the authors' previous work on the EIMC, this leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark conjectures in many new cases.