Some results on finite Drinfeld modules
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Abstract:
Let $\operatorname {K}$ be a global function field, $\infty$ a degree one prime divisor of $\operatorname {K}$ and let $\operatorname {A}$ be the Dedekind domain of functions in $\operatorname {K}$ regular outside $\infty$. Let $\operatorname {H}$ be the Hilbert class field of $\operatorname {A}$, $\operatorname {B}$ the integral closure of $\operatorname {A}$ in $\operatorname {H}$. Let $\psi$ be a rank one normalized Drinfeld $\operatorname {A}$ -module and let $\mathfrak P$ be a prime ideal in $\operatorname {B}$. We explicitly determine the finite $\operatorname {A}$-module structure of $\psi (\operatorname {B} /\mathfrak P^N)$. In particular, if $\operatorname {K} =\mathbb F_q(t)$, $q$ is an odd prime number and $\psi$ is the Carlitz $\mathbb F_q[t]$-module, then the finite $\mathbb F_q[t]$-module $\psi (\mathbb F_q[t]/\mathfrak P^N)$ is always cyclic.References
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Additional Information
- Chih-Nung Hsu
- Affiliation: Department of Mathematics, National Taiwan Normal University, 88 Sec. 4 Ting-Chou Road, Taipei, Taiwan
- Email: maco@math.ntnu.edu.tw
- Received by editor(s): July 23, 1996
- Received by editor(s) in revised form: December 26, 1996
- Communicated by: William W. Adams
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1955-1961
- MSC (1991): Primary 11G09; Secondary 11A05
- DOI: https://doi.org/10.1090/S0002-9939-98-04337-8
- MathSciNet review: 1451807