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arXiv · 2201.09005

Arithmetic Monodromy Groups of Dynamical Belyi maps

Ozlem Ejder
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Abstract

We consider a large family of dynamical Belyi maps of arbitrary degree and study the arithmetic monodromy groups attached to the iterates of such maps. Building on the results of Bouw-Ejder-Karemaker on the geometric monodromy groups of these maps, we show that the quotient of the arithmetic monodromy group by the geometric monodromy group has order either $1$ or $2$. Prior to this article, a result of this kind was only known for quadratic maps (Pink) and a few examples in degree $3$.

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Ozlem Ejder. 2022-01-22. Arithmetic Monodromy Groups of Dynamical Belyi maps. https://arxiv.org/abs/2201.09005

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