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

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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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03769801
Contributor : Filippo A. E. Nuccio Mortarino Majno Di Capriglio Connect in order to contact the contributor
Submitted on : Monday, September 5, 2022 - 5:43:12 PM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM

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  • HAL Id : hal-03769801, version 1

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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-03769801⟩

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