Arithmetic Monodromy Groups of Dynamical Belyi maps
Number Theory
2022-01-25 v1
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 or . Prior to this article, a result of this kind was only known for quadratic maps (Pink) and a few examples in degree .
Keywords
Cite
@article{arxiv.2201.09005,
title = {Arithmetic Monodromy Groups of Dynamical Belyi maps},
author = {Ozlem Ejder},
journal= {arXiv preprint arXiv:2201.09005},
year = {2022}
}
Comments
12 pages, to appear in the Proceedings of the 18th Conference on Arithmetic, Geometry, Cryptography, and Coding Theory