# Isogeny orbits in a family of abelian varieties

Acta Arithmetica (2015)

- Volume: 170, Issue: 2, page 161-173
- ISSN: 0065-1036

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topQian 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 -

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