PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Isogeny orbits in a family of abelian varieties

Volume 170 / 2015

Qian Lin, Ming-Xi Wang Acta Arithmetica 170 (2015), 161-173 MSC: Primary 11G18; Secondary 14K12, 11G50. DOI: 10.4064/aa170-2-4


We prove that if a curve of a nonisotrivial 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 either torsion or contained in a fiber. This result fits into the context of the Zilber–Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.


  • Qian LinCenter of Mathematical Sciences and Applications
    Harvard University
    Cambridge, MA 02138 U.S.A.
  • Ming-Xi WangDepartment of Mathematics
    University of Salzburg
    Hellbrunnerstr. 34/I
    5020 Salzburg, Austria

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image