On the p-rank of an abelian variety and its endomorphism algebra.

Título inglés On the p-rank of an abelian variety and its endomorphism algebra.
Título español El rango p de una variedad abeliana y su álgebra de endomorfismo.
Autor/es González, Josep
Organización Dep. Mat. Apl. Telemàt. Esc. Univ. Politèc. Vilanova i la Geltrú, Vilanova i la Geltrú (Barcelona), España
Revista 0214-1493
Publicación 1998, 42 (1): 119-130, 13 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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, End0(A). As is well known, End0(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 End0(A) are related. For example, if the center of End0(A) is an abelian extension of Q, then A is ordinary if and only if End0(A) is a commutative field. Nevertheless, we give an example in dimension 3 which shows that the algebra End0(A) does not determine the value r(A).
Clasificación UNESCO 120101
Palabras clave español Endomorfismos ; Variedades abelianas ; Rango ; Funciones elípticas
Código MathReviews MR1628150
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