Dynamical Belyi maps and arboreal Galois groups
Dynamical Belyi maps and arboreal Galois groups
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动态 Belyi 地图和树栖伽罗瓦群
DOI：
10.1007/s00229-020-01204-3
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发表时间：
2018
影响因子：
0.6
通讯作者：
V. Karemaker
中科院分区：
文献类型：
--
作者：
I. Bouw;Özlem Ejder;V. Karemaker
我们考虑一个大类的所谓的动力Belyi映射和研究的伽罗瓦群的迭代这样的地图。从组合不变量的地图，我们构建了一个有用的介绍几何伽罗瓦群的子群的自同构群的正规树，在迭代圈产品。使用结果的减少动力Belyi映射模某些素数，我们得到相应的算术伽罗瓦群的迭代。这些导致结果的算术伽罗瓦群的行为下专门化，与应用程序的动态序列。
We 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.