Original scientific paper

Cyclic abelian varieties over finite fields in ordinary isogeny classes

Alejandro José Giangreco ; Aix Marseille Université CNRS, Centrale Marseille, Marseille, France

Abstract

Given an abelian variety A defined over a finite field k, we say that A is cyclic if its group A(k) of rational points is cyclic. In this paper we give a bijection between cyclic abelian varieties of an ordinary isogeny class \(\mathcal{A}\) with Weil polynomial \(f_{\mathcal{A}}\) and some classes of matrices with integer coefficients and having \(f_{\mathcal{A}}\) as characteristic polynomial.

Keywords

group of rational points; cyclic; ordinary abelian variety; finite field; class of matrices

Hrčak ID:

261509

URI

https://hrcak.srce.hr/261509

Publication date:

26.8.2021.

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