On the p-rank of an abelian variety and its endomorphism algebra
González, Josep (Escola Universitària Politècnica de Vilanova i la Geltrú. Departament de Matemàtica Aplicada i Telemàtica)

Date:	1998
Abstract:	Let A be an abelian variety de¯ned over a ¯nite ¯eld. 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 ¯eld. Nevertheless, we give an example in dimension 3 which shows that the algebra End0(A) does not determine the value r(A).
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Publicacions matemàtiques, V. 42 n. 1 (1998) p. 119-130, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/37926
DOI: 10.5565/PUBLMAT_42198_05

12 p, 177.1 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles