Displaying similar documents to “A Note on height pairings on polarized abelian varieties”

Abelian varieties over fields of finite characteristic

Yuri Zarhin (2014)

Open Mathematics

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The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.

Isogeny orbits in a family of abelian varieties

Qian Lin, Ming-Xi Wang (2015)

Acta Arithmetica

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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.