Abstract
In this article we consider Selmer groups and fine Selmer groups of abelian varieties over a number field K. Following a classical approach of Monsky for Iwasawa modules from ideal class groups, we give sufficient conditions for the Iwasawa mu -invariants of the fine Selmer groups and the mu -invariants of the Selmer groups to be bounded as one runs over the mathbb {Z}_p-extensions of K. Moreover, we describe a criterion for the boundedness of Iwasawa lambda -invariants of Selmer groups and fine Selmer groups over multiple mathbb {Z}_p-extensions which generalises a criterion of Monsky from dimension 2 to arbitrary dimension.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
