The characteristic polynomials of abelian varieties of higher dimension over finite fields

JOURNAL OF NUMBER THEORY

卷:196

Article

Hayashida, Daiki¹ 

[1] Kyoto Univ, Grad Sch Sci, Dept Math, Kyoto 6068502, Japan

关键词: Abelian variety;    Finite field;    Weil polynomial;    Characteristic polynomial;   

DOI  :  10.1016/j.jnt.2018.09.014

来源: Elsevier

【 摘 要 】

The characteristic polynomials of abelian varieties over the finite field F-q with q = p(n) elements have a lot of arithmetic and geometric information. They have been explicitly described for abelian varieties up to dimension 4, but little is known in higher dimension. In this paper, among other things, we obtain the following three results on the characteristic polynomial of abelian varieties. First, we prove a relation between n and e, where e is a certain multiplicity associated with a simple abelian variety of arbitrary dimension over F-q. Second, we explicitly describe the characteristic polynomials of simple abelian varieties of arbitrary dimension g, when e = g. Finally, we explicitly describe the coefficients of characteristic polynomials of abelian varieties of dimension 5 over F-q. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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