English

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 11 or 22. Prior to this article, a result of this kind was only known for quadratic maps (Pink) and a few examples in degree 33.

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

R2 v1 2026-06-24T08:58:28.534Z