Isogeny orbits in a family of abelian varieties

Qian Lin Harvard University Ming-Xi Wang University of Salzburg

Publications of CMSA of Harvard mathscidoc: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.
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@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.
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