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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.02688 |
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| _version_ | 1866911036902211584 |
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| author | Chen, Hang |
| author_facet | Chen, Hang |
| contents | Let $F$ be a global function field over the finite field $\mathbb{F}_q$ where $q$ is a prime power and $A$ be the ring of elements in $F$ regular outside $\infty$. Let $ϕ$ be an arbitrary Drinfeld module over $F$ For a fixed non-zero prime ideal $\mathfrak{p}$ of $A$, we show that on the constant $\mathbb{Z}_{\textit{p}}-$extension $\mathfrak{F}$ of $F$, the Pontryagin dual of the fine Selmer group associated to the $\mathfrak{p}-$primary torsion of $ϕ$ over $\mathfrak{F}$ is a finitely generated Iwasawa module such that its Iwasawa $μ-$invariant vanishes. This provides a generalization of the results given in arXiv:2311.06499. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $μ-$invariant of fine Selmer groups associated to general Drinfeld modules Chen, Hang Number Theory Let $F$ be a global function field over the finite field $\mathbb{F}_q$ where $q$ is a prime power and $A$ be the ring of elements in $F$ regular outside $\infty$. Let $ϕ$ be an arbitrary Drinfeld module over $F$ For a fixed non-zero prime ideal $\mathfrak{p}$ of $A$, we show that on the constant $\mathbb{Z}_{\textit{p}}-$extension $\mathfrak{F}$ of $F$, the Pontryagin dual of the fine Selmer group associated to the $\mathfrak{p}-$primary torsion of $ϕ$ over $\mathfrak{F}$ is a finitely generated Iwasawa module such that its Iwasawa $μ-$invariant vanishes. This provides a generalization of the results given in arXiv:2311.06499. |
| title | The $μ-$invariant of fine Selmer groups associated to general Drinfeld modules |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.02688 |