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arXiv · 1803.04946

On a conjecture of Buium and Poonen

Gregorio Baldi
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Abstract

Given a correspondence between a modular curve $S$ and an elliptic curve $A$, we prove that the intersection of any finite-rank subgroup of $A$ with the set of points on $A$ corresponding to an isogeny class on $S$ 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.

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Gregorio Baldi. 2018-03-13. On a conjecture of Buium and Poonen. https://doi.org/10.5802/aif.3317

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