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arXiv · 1708.03036

Belyi's theoerm in characteristic two

Yusuke Sugiyama·Seidai Yasuda
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Abstract

We prove an analogue of Belyi's theorem in characteristic two. Our proof consists of the following three steps. We first introduce a new notion called "pseudo-tame" for morphisms between curves over an algebraically closed field of characteristic two. Secondly, we prove the existence of a "pseudo-tame" rational function by proving vanishing of an obstruction class. Finally we will construct a tamely ramified rational function from the "pseudo-tame" rational function.

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Yusuke Sugiyama, Seidai Yasuda. 2017-08-10. Belyi's theoerm in characteristic two. https://doi.org/10.1112/s0010437x19007723

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