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Belyi’s theorem in characteristic two

  • Yusuke Sugiyama (a1) and Seidai Yasuda (a2)

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-tameness for morphisms between curves over an algebraically closed field of characteristic two. Secondly, we prove the existence of a ‘pseudo-tame’ rational function by showing the vanishing of an obstruction class. Finally, we construct a tamely ramified rational function from the ‘pseudo-tame’ rational function.

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Belyi’s theorem in characteristic two

  • Yusuke Sugiyama (a1) and Seidai Yasuda (a2)

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