A Study of Fine Selmer Groups Over Function Fields via Greenberg Neighbourhoods
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909662231658496 |
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| author | Ghosh, Sohan |
| author_facet | Ghosh, Sohan |
| contents | Greenberg examined the local behavior of Iwasawa invariants as functions on the the set of all $\mathbb{Z}_p$-extensions of a number field $F$. Kleine later extended these ideas to explore the variation of Iwasawa invariants in the context of Selmer groups of elliptic curves across different $\mathbb{Z}_p$-extensions of $F$. Let $K$ be a global function field of characteristic $p$. In this article, we investigate the relation between Iwasawa invariants of fine Selmer groups of an elliptic curve over $K$ across various $\mathbb{Z}_p$-extensions of $K$, utilizing Kleine's techniques. Furthermore, we connect this analysis to an analogue of Conjecture A by Coates and Sujatha for different $\mathbb{Z}_p$-extensions of the function field $K$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_22002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Study of Fine Selmer Groups Over Function Fields via Greenberg Neighbourhoods Ghosh, Sohan Number Theory Primary: 11R23, Secondary: 20C07, 11G05, 11R58 Greenberg examined the local behavior of Iwasawa invariants as functions on the the set of all $\mathbb{Z}_p$-extensions of a number field $F$. Kleine later extended these ideas to explore the variation of Iwasawa invariants in the context of Selmer groups of elliptic curves across different $\mathbb{Z}_p$-extensions of $F$. Let $K$ be a global function field of characteristic $p$. In this article, we investigate the relation between Iwasawa invariants of fine Selmer groups of an elliptic curve over $K$ across various $\mathbb{Z}_p$-extensions of $K$, utilizing Kleine's techniques. Furthermore, we connect this analysis to an analogue of Conjecture A by Coates and Sujatha for different $\mathbb{Z}_p$-extensions of the function field $K$. |
| title | A Study of Fine Selmer Groups Over Function Fields via Greenberg Neighbourhoods |
| topic | Number Theory Primary: 11R23, Secondary: 20C07, 11G05, 11R58 |
| url | https://arxiv.org/abs/2506.22002 |