The $μ-$invariant of fine Selmer groups associated to general Drinfeld modules
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911036902211584 |
|---|---|
| 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 |