Cyclic abelian varieties over finite fields in ordinary isogeny classes

Alejandro José Giangreco

Vol. 26 No. 2 (2021)

Regular Articles

Cyclic abelian varieties over finite fields in ordinary isogeny classes

Published 2021-07-19

Alejandro José Giangreco

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Abstract

Given an abelian variety $A$ defined over a finite field $k$, we say that $A$ is \emph{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

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