{
"id": "1803.04946",
"version": "v1",
"published": "2018-03-13T17:29:14.000Z",
"updated": "2018-03-13T17:29:14.000Z",
"title": "On a conjecture of Buium and Poonen",
"authors": [
"Gregorio Baldi"
],
"comment": "Comments are welcome",
"categories": [
"math.NT"
],
"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 problem was conjectured 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.",
"revisions": [
{
"version": "v1",
"updated": "2018-03-13T17:29:14.000Z"
}
],
"analyses": {
"keywords": [
"serres open image theorem",
"elliptic curve",
"zilber-pink conjecture",
"finite-rank subgroup",
"shimura varieties"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}