Surjectivity of the adelic Galois Representation associated to a Drinfeld Module of prime rank
| Autor: | Chen, Chien-Hua |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, let $\phi$ be the Drinfeld module over $\mathbb{F}_{q}(T)$ of prime rank $r$ defined by $$\phi_T=T+\tau^{r-1}+T^{q-1}\tau^r.$$ We prove that under certain condition on $\mathbb{F}_q$, the adelic Galois representation $${\rho}_{\phi}:{\rm{Gal}}(\mathbb{F}_q(T)^{{\rm{sep}}}/\mathbb{F}_q(T))\longrightarrow \varprojlim_{\mathfrak{a}}{\rm{Aut}}(\phi[\mathfrak{a}])\cong {\rm{GL_r}}(\widehat{A})$$ is surjective. |
| Databáze: | arXiv |
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