FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 2, PAGES 25-43

Prime numbers of bad reduction for dessins of genus $0$

A. M. Vashevnik

Abstract

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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.

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Last modified: June 9, 2005