Qian LinHarvard UniversityMing-Xi WangUniversity of Salzburg
Publications of CMSA of Harvardmathscidoc:1702.38033
We prove that if a curve of a non-isotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety then it is special. This result fits into the context of Zilber-Pink conjecture and partially generalizes a result of Faltings. Moreover by using the polyhedral reduction theory we give a new proof of a result of Bertrand.
@inproceedings{qianisogeny,
title={Isogeny orbits in a family of abelian varieties},
author={Qian Lin, and Ming-Xi Wang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207031117963716233},
}
Qian Lin, and Ming-Xi Wang. Isogeny orbits in a family of abelian varieties. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207031117963716233.