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 . In the postcritically infinite case, the proof uses algebraic techniques, including a result concerning ramification in towers of cyclic -extensions. In the postcritically finite case, the proof uses the theory of heights together with results of Amoroso and Zannier and Amoroso and Dvornicich, as well as properties of the Arakelov–Zhang pairing.
Citation
Jesse Andrews. Clayton Petsche. "Abelian extensions in dynamical Galois theory." Algebra Number Theory 14 (7) 1981 - 1999, 2020. https://doi.org/10.2140/ant.2020.14.1981
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