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arXiv · 1811.02595

On Belyi's Theorem in positive characteristic

Kirti Joshi
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Abstract

The famous theorem of Belyi can be viewed as a characterization of compact Riemann surfaces which admit a non-empty open subset uniformized by a subgroup of $SL_2(\mathbb{Z})$ of finite index. I show that if $q\geq 5$, then ${\bf F}_q(T)$ is the one and only function field of positive characteristic for which such an analogous characterization of rigid analytic spaces of dimension one can exist and that Drinfel$'$d modular curves provide examples of rigid analytic spaces of this type.

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Kirti Joshi. 2018-11-06. On Belyi's Theorem in positive characteristic. https://arxiv.org/abs/1811.02595

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