On Subvarieties of Abelian Varieties.
Ziv Ran (1980/81)
Inventiones mathematicae
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Displaying similar documents to “A note on abelian varieties embedded in quadrics”
On Subvarieties of Abelian Varieties.
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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.
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Leonard Roth (1954)
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A Note on height pairings on polarized abelian varieties
Valerio Talamanca (1999)
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Let be an abelian variety defined over a number field . In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.