论文标题
一项关于阿贝尔动力学群组组的调查
A survey on abelian dynamical Galois groups
论文作者
论文摘要
令$ k $为一个数字字段，$ f \ in k [x] $，$α\ in K $。最新的猜想是安德鲁斯和Petsche的一个预测，当且仅当对$（f，α）$是$ k^{\ text {ab}} $时，这对$（f，α）$的动态galois组为ABELIAN $ζ+ζ^{ - 1} $，$ζ$是统一的根源。我们回顾了三种完全不同的方法，可以证明猜想的几种情况。
Let $K$ be a number field, $f\in K[x]$ and $α\in K$. A recent conjecture of Andrews and Petsche predicts that the dynamical Galois group of the pair $(f,α)$ is abelian if and only if the pair $(f,α)$ is $K^{\text{ab}}$-conjugated to $(g,β)$, where $g$ is a power or a Chebyshev map and $β$ is $ζ$ or $ζ+ζ^{-1}$, respectively, and $ζ$ is a root of unity. We review three completely different approaches that allow to prove several cases of the conjecture.
