On the surjectivity of $(T)$-adic Galois Representations of Drinfeld $A$-Modules of Rank 2 and 3: Density results
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914482913017856 |
|---|---|
| author | Kumar, Narasimha Shit, Dwipanjana |
| author_facet | Kumar, Narasimha Shit, Dwipanjana |
| contents | Let $\mathbb{F}_{q}$ be a finite field, and $A:=\mathbb{F}_{q}[T]$. In this article, we give explicit criteria, involving concrete valuations, on the coefficients of the Drinfeld $A$-modules of rank $r$ for $r=2,3$, which ensure the surjectivity of the associated $(T)$-adic Galois representation. As a result, we shall calculate the densities of such Drinfeld $A$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15915 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the surjectivity of $(T)$-adic Galois Representations of Drinfeld $A$-Modules of Rank 2 and 3: Density results Kumar, Narasimha Shit, Dwipanjana Number Theory Primary 11G09, 11F80, Secondary 11R45 Let $\mathbb{F}_{q}$ be a finite field, and $A:=\mathbb{F}_{q}[T]$. In this article, we give explicit criteria, involving concrete valuations, on the coefficients of the Drinfeld $A$-modules of rank $r$ for $r=2,3$, which ensure the surjectivity of the associated $(T)$-adic Galois representation. As a result, we shall calculate the densities of such Drinfeld $A$-modules. |
| title | On the surjectivity of $(T)$-adic Galois Representations of Drinfeld $A$-Modules of Rank 2 and 3: Density results |
| topic | Number Theory Primary 11G09, 11F80, Secondary 11R45 |
| url | https://arxiv.org/abs/2604.15915 |