Structure of fine Selmer groups in abelian p-adic Lie extensions

Authors

Debanjana Kundu, The University of Texas Rio Grande Valley
Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio
Sujatha Ramdorai

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

Recommended Citation

Kundu, Debanjana, Filippo Alberto Edoardo Nuccio Mortarino Majno, Di Capriglio, and Sujatha Ramdorai. "Structure of fine Selmer groups in abelian $ p $-adic Lie extensions." Osaka Journal of Mathematics 61, no. 1 (2024): 121-146.

Publication Title

Osaka Journal of Mathematics