Structure of fine Selmer groups in abelian p-adic Lie extensions - CNRS - Centre national de la recherche scientifique
Pré-Publication, Document De Travail Année : 2022

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

Résumé

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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Dates et versions

hal-03769801 , version 1 (05-09-2022)
hal-03769801 , version 2 (21-11-2022)
hal-03769801 , version 3 (16-01-2023)
hal-03769801 , version 4 (21-04-2023)
hal-03769801 , version 5 (05-02-2024)

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  • HAL Id : hal-03769801 , version 3

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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. 2022. ⟨hal-03769801v3⟩
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