This article is cited in 4 papers

Prime numbers of bad reduction for dessins of genus 0

A. M. Vashevnik

M. V. Lomonosov Moscow State University

Abstract: This article expands the special case of the Grothendieck theory to arbitrary fields. A formal definition of Belyi function over an arbitrary field is introduced. It turns out that the properties of Belyi functions over finite fields and the properties of classical Belyi functions are quite different. A definition of the primes of bad reduction is also given, and the primes of bad reduction are calculated for some dessin families.

UDC: 512.624.3

 English version: Journal of Mathematical Sciences (New York), 2007, 142:2, 1883–1894

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