On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture
Number Theory
2018-08-06 v3
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.
Keywords
Cite
@article{arxiv.1509.00200,
title = {On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture},
author = {Henri Johnston and Andreas Nickel},
journal= {arXiv preprint arXiv:1509.00200},
year = {2018}
}
Comments
33 pages; to appear in Mathematische Zeitschrift; v3 many minor updates including new title; v2 some cohomological arguments simplified; v1 is a revised version of the second half of arXiv:1408.4934v2