Fields of definition of dynamical systems on ℙ¹. Improvements on a result of Silverman

2024/05/06 by Giulio Bresciani, Bresciani, Giulio
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2405.03612

openalex publication_date 2024/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

J. Silverman proved that a dynamical system on ℙ¹ 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 ℙ¹ descend to the field of moduli.

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