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

Debanjana Kundu; Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio; Sujatha Ramdorai

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arXiv · 2304.10938

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

Debanjana Kundu·Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio·Sujatha Ramdorai

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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.

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Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai. 2023-04-21. Structure of fine Selmer groups in abelian p-adic Lie extensions. https://arxiv.org/abs/2304.10938

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