Isogeny orbits in a family of abelian varieties

Qian Lin, and Ming-Xi Wang. "Isogeny orbits in a family of abelian varieties." Acta Arithmetica 170.2 (2015): 161-173. <http://eudml.org/doc/279370>.

@article{QianLin2015,
abstract = {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.},
author = {Qian Lin, Ming-Xi Wang},
journal = {Acta Arithmetica},
keywords = {abelian variety; Siegel modular variety; isogeny; Faltings height; canonical height; polyhedral reduction theory; Silverman's specialization theorem},
language = {eng},
number = {2},
pages = {161-173},
title = {Isogeny orbits in a family of abelian varieties},
url = {http://eudml.org/doc/279370},
volume = {170},
year = {2015},
}

TY - JOUR
AU - Qian Lin
AU - Ming-Xi Wang
TI - Isogeny orbits in a family of abelian varieties
JO - Acta Arithmetica
PY - 2015
VL - 170
IS - 2
SP - 161
EP - 173
AB - 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.
LA - eng
KW - abelian variety; Siegel modular variety; isogeny; Faltings height; canonical height; polyhedral reduction theory; Silverman's specialization theorem
UR - http://eudml.org/doc/279370
ER -