Author:
Bouw Irene I.,Ejder Özlem,Karemaker Valentijn
Abstract
AbstractWe consider a large class of so-called dynamical Belyi maps and study the Galois groups of iterates of such maps. From the combinatorial invariants of the maps, we construct a useful presentation of the geometric Galois groups as subgroups of automorphism groups of regular trees, in terms of iterated wreath products. Using results on the reduction of dynamical Belyi maps modulo certain primes, we obtain results on the corresponding arithmetic Galois groups of iterates. These lead to results on the behavior of the arithmetic Galois groups under specialization, with applications to dynamical sequences.
Publisher
Springer Science and Business Media LLC
Cited by
2 articles.
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1. Settled elements in profinite groups;Advances in Mathematics;2022-08
2. Arithmetic monodromy groups of dynamical Belyi maps;Arithmetic, Geometry, Cryptography, and Coding Theory 2021;2022