On a conjecture of Buium and Poonen
Number Theory
2021-10-05 v3
Abstract
Given a correspondence between a modular curve and an elliptic curve , we prove that the intersection of any finite-rank subgroup of with the set of points on corresponding to an isogeny class on is finite. The question was proposed by A. Buium and B. Poonen in 2009. We follow the strategy proposed by the authors, using a result about the equidistribution of Hecke points on Shimura varieties and Serre's open image theorem. The result is an instance of the Zilber-Pink conjecture.
Keywords
Cite
@article{arxiv.1803.04946,
title = {On a conjecture of Buium and Poonen},
author = {Gregorio Baldi},
journal= {arXiv preprint arXiv:1803.04946},
year = {2021}
}
Comments
To appear in Annales de l'Institut Fourier