Structure of fine Selmer groups in abelian p-adic Lie extensions
Number Theory
2024-02-07 v2
Abstract
This paper studies fine Selmer groups of elliptic curves in abelian -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 -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.
Keywords
Cite
@article{arxiv.2304.10938,
title = {Structure of fine Selmer groups in abelian p-adic Lie extensions},
author = {Debanjana Kundu and Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio and Sujatha Ramdorai},
journal= {arXiv preprint arXiv:2304.10938},
year = {2024}
}