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

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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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Dates and versions

hal-03769801 , version 1 (05-09-2022)
hal-03769801 , version 2 (21-11-2022)
hal-03769801 , version 3 (16-01-2023)

Licence

Attribution - CC BY 4.0

Identifiers

  • HAL Id : hal-03769801 , version 3

Cite

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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