A class of Drinfeld $A$-modules of rank $3$ with surjective Galois representations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914075769831424 |
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| author | Kumar, Narasimha Shit, Dwipanjana |
| author_facet | Kumar, Narasimha Shit, Dwipanjana |
| contents | Let $q = p^e \geq 7$ be an odd prime power, and set $A := \mathbb{F}_q[T]$. In this article, we construct an infinite two-parameter family of Drinfeld $A$-modules of rank $3$ such that, for every non-zero prime ideal $\mathfrak{l}$ of $A$, the associated mod-$\mathfrak{l}$, $\mathfrak{l}$-adic, and adelic Galois representations are surjective. These results generalise the specific example, constructed only for primes $p\equiv 1\pmod{3}$, in~\cite{Che22}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A class of Drinfeld $A$-modules of rank $3$ with surjective Galois representations Kumar, Narasimha Shit, Dwipanjana Number Theory Primary 11G09, 11F80, Secondary 11C08 Let $q = p^e \geq 7$ be an odd prime power, and set $A := \mathbb{F}_q[T]$. In this article, we construct an infinite two-parameter family of Drinfeld $A$-modules of rank $3$ such that, for every non-zero prime ideal $\mathfrak{l}$ of $A$, the associated mod-$\mathfrak{l}$, $\mathfrak{l}$-adic, and adelic Galois representations are surjective. These results generalise the specific example, constructed only for primes $p\equiv 1\pmod{3}$, in~\cite{Che22}. |
| title | A class of Drinfeld $A$-modules of rank $3$ with surjective Galois representations |
| topic | Number Theory Primary 11G09, 11F80, Secondary 11C08 |
| url | https://arxiv.org/abs/2510.04007 |