Kummer theory of abelian varieties and reductions of Mordell-Weil groups
Tom Weston (2003)
Acta Arithmetica
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Tom Weston (2003)
Acta Arithmetica
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G. Faltings (1983)
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Joseph H. Silverman (1985)
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Giambattista Marini (1997)
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Werner Bauer (1992)
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Ziv Ran (1980/81)
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Grzegorz Banaszak, Piotr Krasoń (2011)
Acta Arithmetica
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W. Casselman (1971)
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J.S. Milne (1972)
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Alice Silverberg (1985)
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Takashi Ichikawa (1991)
Mathematische Annalen
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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.
Takashi Fukuda, Keiichi Komatsu, Shuji Yamagata (2007)
Acta Arithmetica
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