Torsion points on abelian varieties of CM-type
Alice Silverberg (1988)
Compositio Mathematica
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Alice Silverberg (1988)
Compositio Mathematica
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D. W. Masser, G. Wüstholz (1995)
Publications Mathématiques de l'IHÉS
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D. W. Masser (1984)
Compositio Mathematica
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J. H. Silverman, J. F. Voloch (1991)
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.
Marcel Jacobson, Moshe Jarden (2001)
Acta Arithmetica
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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...
Olivier Debarre (1994)
Bulletin de la Société Mathématique de France
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