Structure of fine Selmer groups in abelian p-adic Lie extensions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917583196782592 |
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| author | Kundu, Debanjana Di Capriglio, Filippo Alberto Edoardo Nuccio Mortarino Majno Ramdorai, Sujatha |
| author_facet | Kundu, Debanjana Di Capriglio, Filippo Alberto Edoardo Nuccio Mortarino Majno Ramdorai, Sujatha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Structure of fine Selmer groups in abelian p-adic Lie extensions Kundu, Debanjana Di Capriglio, Filippo Alberto Edoardo Nuccio Mortarino Majno Ramdorai, Sujatha Number Theory 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. |
| title | Structure of fine Selmer groups in abelian p-adic Lie extensions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2304.10938 |