论文标题
动力学贝利图算术单构图
Arithmetic Monodromy Groups of Dynamical Belyi maps
论文作者
论文摘要
我们考虑了一个任意程度的一大批动态贝利图，并研究了附在此类地图的迭代元中的算术单构群。在这些地图的几何单组群上Bouw-ejder-karemaker的结果建立在基础上，我们表明，几何单模型组的算术单片组的商具有$ 1 $或$ 2 $的订单。在本文之前，此类结果仅以二次地图（粉红色）而闻名，并以$ 3 $ $ 3的示例闻名。
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 $3$.
