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arXiv · 2001.00659

Abelian extensions in dynamical Galois theory

Jesse Andrews·Clayton Petsche
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Abstract

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.

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BibTeXRIS

Jesse Andrews, Clayton Petsche. 2021-10-07. Abelian extensions in dynamical Galois theory. https://doi.org/10.2140/ant.2020.14.1981

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