دورية أكاديمية
On the $p$-rank of an abelian variety and its endomorphism algebra
| العنوان: | On the $p$-rank of an abelian variety and its endomorphism algebra |
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| المؤلفون: | González, J. |
| المصدر: | Publicacions Matemàtiques; Vol. 42, Núm. 1 (1998); p. 119-130 |
| حالة النشر: | published |
| بيانات النشر: | Publicacions Matemàtiques, 1998. |
| سنة النشر: | 1998 |
| الوصف: | 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, $\operatorname{End}^0(A)$. As is well known, $\operatorname{End}^0(A)$ determines $r(A)$ when $A$ is an elliptic curve. We show that, under some conditions, the value of $r(A)$ and the structure of $\operatorname{End}^0(A)$ are related. For example, if the center of $\operatorname{End}^0(A)$ is an abelian extension of $\Bbb Q$, then $A$ is ordinary if and only if $\operatorname{End}^0(A)$ is a commutative field. Nevertheless, we give an example in dimension 3 which shows that the algebra $\operatorname{End}^0(A)$ does not determine the value $r(A)$. |
| نوع الوثيقة: | article |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 2014-4350 0214-1493 |
| العلاقة: | https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/37926/40411Test |
| DOI: | 10.5565/37926 |
| الوصول الحر: | https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/37926Test |
| رقم الانضمام: | edsrac.37926 |
| قاعدة البيانات: | RACO (Revistes Catalanes amb Accés Obert) |
| تدمد: | 20144350 02141493 |
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| DOI: | 10.5565/37926 |