English

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.

Keywords

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

R2 v1 2026-06-28T07:59:08.104Z