Fields of definition of dynamical systems on $\mathbb{P}^{1}$. Improvements on a result of Silverman

Giulio Bresciani

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arXiv · 2405.03612

Fields of definition of dynamical systems on $\mathbb{P}^{1}$. Improvements on a result of Silverman

Giulio Bresciani

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Abstract

J. Silverman proved that a dynamical system on $\mathbb{P}^{1}$ descends to the field of moduli if it is polynomial or it has even degree, but for non-polynomial ones of odd degree the picture is less clear. We give a complete characterization of which dynamical systems over $\mathbb{P}^{1}$ descend to the field of moduli.

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Giulio Bresciani. 2024-05-06. Fields of definition of dynamical systems on $\mathbb{P}^{1}$. Improvements on a result of Silverman. https://arxiv.org/abs/2405.03612

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