Surjectivity of the adelic Galois Representation associated to a Drinfeld Module of prime rank

arXiv2111.04234MaRDI QIDQ6382438

Chien-Hua Chen

Publication date: 7 November 2021

Abstract: In this paper, let $phi$ be the Drinfeld module over $mathbb{F}_q(T)$ of prime rank $r$ defined by ${\displaystyle }$phi_T=T+ au^{r-1}+T^{q-1} au^r.${\displaystyle }$ We prove that under certain condition on $mathbb{F}_q$, the adelic Galois representation ${\displaystyle }${ ho}_{phi}:{ m{Gal}}(mathbb{F}_q(T)^{{ m{sep}}}/mathbb{F}_q(T))longrightarrow varprojlim_{mathfrak{a}}{ m{Aut}}(phi[mathfrak{a}])cong { m{GL_r}}(widehat{A})${\displaystyle }$ is surjective.

This page was built for publication: Surjectivity of the adelic Galois Representation associated to a Drinfeld Module of prime rank

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6382438)