Belyi's theorems in positive characteristic
Anbar Meidl, Nurdagül and Tutdere, Seher (2020) Belyi's theorems in positive characteristic. International Journal of Number Theory, 16 (6). pp. 1355-1368. ISSN 1793-0421 (Print) 1793-7310 (Online)
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Official URL: http://dx.doi.org/10.1142/S1793042120500712
There are two types of Belyi’s Theorem for curves deﬁned over ﬁnite ﬁelds of characteristic p, namely the Wild and the Tame p-Belyi Theorems. In this paper, we discuss them in the language of function ﬁelds. In particular, we provide a constructive proof for the existence of a pseudo-tame element introduced in , which leads to a self-contained proof for the Tame 2-Belyi Theorem. Moreover, we provide uniﬁed and simple proofs for Belyi Theorems unlike the known ones that use technical results from Algebraic Geometry.
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