Displaying similar documents to “Iwasawa-theory of abelian varieties at primes of non-ordinary reduction.”

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...