A construction of an abelian variety with a given endomorphism algebra
F. Oort, M. Van der Put (1988)
Compositio Mathematica
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F. Oort, M. Van der Put (1988)
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Hans-Georg Rück (1990)
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Alice Silverberg (1988)
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Josep González (1998)
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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...
D. W. Masser, G. Wüstholz (1995)
Publications Mathématiques de l'IHÉS
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William C. Waterhouse (1969)
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J. H. Silverman, J. F. Voloch (1991)
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