Relations among modular points on elliptic curves
Number Theory
2017-04-03 v1
Abstract
Given a correspondence between a modular curve and an elliptic curve A we study the group of relations among the CM points of A. In particular we prove that the intersection of any finite rank subgroup of A with the set of CM points of A is finite. We also prove a local version of this global result with an effective bound valid also for certain infinite rank subgroups. We deduce the local result from a ``reciprocity'' theorem for CL (canonical lift) points on A. Furthermore we prove similar global and local results for intersections between subgroups of A and isogeny classes in A. Finally we prove Shimura curve analogues and, in some cases, higher-dimensional versions of these results.
Cite
@article{arxiv.0706.0566,
title = {Relations among modular points on elliptic curves},
author = {Alexandru Buium and Bjorn Poonen},
journal= {arXiv preprint arXiv:0706.0566},
year = {2017}
}