Quadratic points on dynamical modular curves

2023/01/02 by Doyle, John R., Krumm, David · 1 citation
#11G30 #14G05 #37P35 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Primary 37P05 #Secondary 37P15

paper · doi:10.48550/arxiv.2301.00510

Abstract

Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This yields a classification statement on preperiodic points for quadratic polynomials over quadratic fields, extending previous work of Poonen, Faber, and the authors.

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• Cubic points on dynamical modular curves

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