Factorization estimates for abelian varieties
D. W. Masser, G. Wüstholz (1995)
Publications Mathématiques de l'IHÉS
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D. W. Masser, G. Wüstholz (1995)
Publications Mathématiques de l'IHÉS
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Tom Weston (2003)
Acta Arithmetica
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Ziv Ran (1980/81)
Inventiones mathematicae
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Joseph H. Silverman (1985)
Inventiones mathematicae
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Josep González (1998)
Publicacions Matemàtiques
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Let A be an abelian variety defined over a finite field. In this paper, we discuss the relationship between the p-rank of A, r(A), and its endomorphism algebra, End(A). As is well known, End(A) determines r(A) when A is an elliptic curve. We show that, under some conditions, the value of r(A) and the structure of End(A) are related. For example, if the center of End(A) is an abelian extension of Q, then A is ordinary if and only if End(A) is a commutative field. Nevertheless, we give...
Alice Silverberg (1988)
Compositio Mathematica
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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.
Valerio Talamanca (1999)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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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.
F. Oort, M. Van der Put (1988)
Compositio Mathematica
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Giambattista Marini (1997)
Manuscripta mathematica
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Everett W. Howe (1995)
Journal für die reine und angewandte Mathematik
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