Quadratic points on dynamical modular curves
Number Theory
2023-01-24 v2 Algebraic Geometry
Dynamical Systems
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.
Cite
@article{arxiv.2301.00510,
title = {Quadratic points on dynamical modular curves},
author = {John R. Doyle and David Krumm},
journal= {arXiv preprint arXiv:2301.00510},
year = {2023}
}
Comments
Improvements to the exposition; stronger version of what is now Proposition 4.5