On Belyi's Theorem in positive characteristic
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866916727126753280 |
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| author | Joshi, Kirti |
| author_facet | Joshi, Kirti |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_02595 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On Belyi's Theorem in positive characteristic Joshi, Kirti Algebraic Geometry Number Theory 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. |
| title | On Belyi's Theorem in positive characteristic |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/1811.02595 |