Stark units and main conjectures for totally real fields
Number Theory
2019-02-20 v1
Abstract
Main theorem of [Buyukboduk, arXiv:0706.0377v1] suggests that it should be possible to lift the Kolyvagin systems of Stark units constructed in [Buyukboduk, arXiv:math/0703426v1] to a Kolyvagin system over the cyclotomic Iwasawa algebra. This is what we prove in this paper. This construction gives the first example towards a more systematic study of Kolyvagin system theory over an Iwasawa algebra when the core Selmer rank is greater than one. As a result of this construction, we reduce the main conjectures of Iwasawa theory for totally real fields to a statement of local Iwasawa theory. This statement, however, turns out to be interesting in its own right as it suggests a relation between solutions to -adic and complex Stark conjectures.
Keywords
Cite
@article{arxiv.0706.3087,
title = {Stark units and main conjectures for totally real fields},
author = {Kazim Buyukboduk},
journal= {arXiv preprint arXiv:0706.3087},
year = {2019}
}