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January 2024 Structure of fine Selmer groups in abelian $p$-adic Lie extensions
Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai
Author Affiliations +
Osaka J. Math. 61(1): 121-146 (January 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 $\mathbb{Z}_p$-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.

Acknowledgments

D.K. is supported by a PIMS Postdoctoral fellowship. S.R. is supported by the NSERC Discovery Grant 2019-03987. We thank the referee for their timely and thorough reading of the manuscript which helped strengthen some of the results and also contributed to a clearer exposition.

Citation

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Debanjana Kundu. Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio. Sujatha Ramdorai. "Structure of fine Selmer groups in abelian $p$-adic Lie extensions." Osaka J. Math. 61 (1) 121 - 146, January 2024.

Information

Received: 21 September 2022; Revised: 26 December 2022; Published: January 2024
First available in Project Euclid: 12 January 2024

Subjects:
Primary: 11R23
Secondary: 11R34

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

Vol.61 • No. 1 • January 2024
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