On supersingular curves and Abelian varieties.
Torsten Ekedahl (1987)
Mathematica Scandinavica
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Displaying similar documents to “On abelian varieties associated with elliptic curves with complex multiplication”
On supersingular curves and Abelian varieties.
Some Curves in Abelian Varieties.
R.C. Gunning (1982)
Inventiones mathematicae
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Some density results for curves with non-simple jacobians.
E. Colombo, G.P. Pirola (1990)
Mathematische Annalen
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On the p-rank of an abelian variety and its endomorphism algebra.
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...
Kummer theory of abelian varieties and reductions of Mordell-Weil groups
Tom Weston (2003)
Acta Arithmetica
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On Subvarieties of Abelian Varieties.
Ziv Ran (1980/81)
Inventiones mathematicae
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The K.P. Hypothesis for decomposable Abelian Varieties.
Giambattista Marini (1997)
Manuscripta mathematica
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On the problem of detecting linear dependence for products of abelian varieties and tori
Antonella Perucca (2010)
Acta Arithmetica
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Improperly abelian varieties
Leonard Roth (1954)
Rendiconti del Seminario Matematico della Università di Padova
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A remark on certain simultaneous divisibility sequences
Stefan Barańczuk, Piotr Rzonsowski (2014)
Colloquium Mathematicae
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We investigate possible orders of reductions of a point in the Mordell-Weil groups of certain abelian varieties and in direct products of the multiplicative group of a number field. We express the result obtained in terms of divisibility sequences.
Lifting Abelian Varieties.
Peter Norman (1981)
Inventiones mathematicae
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Arakelov's Theorem for Abelian Varieties.
G. Faltings (1983)
Inventiones mathematicae
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The exponent of an abelian subvariety.
Herbert Lange, Christina Birkenhake (1991)
Mathematische Annalen
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On the number of points on abelian and Jacobian varieties over finite fields
Yves Aubry, Safia Haloui, Gilles Lachaud (2013)
Acta Arithmetica
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We give upper and lower bounds for the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces.