Visibility of the Shafarevich-Tate group at higher level.
Jetchev, Dimitar P., Stein, William A. (2007)
Documenta Mathematica
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Jetchev, Dimitar P., Stein, William A. (2007)
Documenta Mathematica
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Loïc Merel (1999)
Journal de théorie des nombres de Bordeaux
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We give a survey of methods used to connect the study of ternary diophantine equations to modern techniques coming from the theory of modular forms.
Kenneth A. Ribet (1990)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Darmon, Henri (1999)
Annals of Mathematics. Second Series
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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.
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...
Watkins, Mark (2002)
Experimental Mathematics
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Kenneth A. Ribet (1980)
Mathematische Annalen
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Barry Mazur (1977)
Publications Mathématiques de l'IHÉS
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Dummigan, Neil (2002)
Experimental Mathematics
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Massimo Bertolini (1997)
Collectanea Mathematica
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