Cubic points on dynamical modular curves

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Doyle, John R., Galarraga, Alexander
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915618893070336
author Doyle, John R.
Galarraga, Alexander
author_facet Doyle, John R.
Galarraga, Alexander
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_11491
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Cubic points on dynamical modular curves
Doyle, John R.
Galarraga, Alexander
Number Theory
Algebraic Geometry
Dynamical Systems
37P15, 37P35 (Primary) 11G30, 14G05 (Secondary)
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.
title Cubic points on dynamical modular curves
topic Number Theory
Algebraic Geometry
Dynamical Systems
37P15, 37P35 (Primary) 11G30, 14G05 (Secondary)
url https://arxiv.org/abs/2511.11491