论文标题
动态galo理论中的阿贝尔扩展
Abelian extensions in dynamical Galois theory
论文作者
论文摘要
我们提出了与多项式相关的动态GALOIS组何时是Abelian的猜想表征，我们在几种情况下证明了我们的猜想，包括$ {\ Mathbb Q} $的稳定二次案例。在后批判性无限的情况下，该证明使用代数技术，其中包括有关循环$ p $延伸的塔的结果的结果。在后有限的情况下，证明使用高度理论以及Amoroso-Zannier和Amoroso-Dvornicich的结果，以及Arakelov-Zhang配对的特性。
We propose a conjectural characterization of when the dynamical Galois group associated to a polynomial is abelian, and we prove our conjecture in several cases, including the stable quadratic case over ${\mathbb Q}$. In the postcritically infinite case, the proof uses algebraic techniques, including a result concerning ramification in towers of cyclic $p$-extensions. In the postcritically finite case, the proof uses the theory of heights together with results of Amoroso-Zannier and Amoroso-Dvornicich, as well as properties of the Arakelov-Zhang pairing.
