School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Document Type

Article

Publication Date

1-2024

Abstract

This paper studies fine Selmer groups of elliptic curves in abelian p -adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Z p -extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg's Conjecture is clarified.

Comments

Copyright © 2024 Osaka University and Osaka Metropolitan University, Departments of Mathematics

Publication Title

Osaka Journal of Mathematics

Included in

Mathematics Commons

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