Cubic points on dynamical modular curves
Number Theory
2025-11-17 v1 Algebraic Geometry
Dynamical Systems
Abstract
We consider the family of dynamical modular curves associated to quadratic polynomial maps and determine precisely which of these curves have infinitely many cubic points. We use this to prove a classification statement on preperiodic points for quadratic polynomials over cubic fields, extending previous work of Poonen, Faber, and the first author and Krumm.
Cite
@article{arxiv.2511.11491,
title = {Cubic points on dynamical modular curves},
author = {John R. Doyle and Alexander Galarraga},
journal= {arXiv preprint arXiv:2511.11491},
year = {2025}
}
Comments
36 pages