Cyclic abelian varieties over finite fields in ordinary isogeny classes

Alejandro J. Giangreco-Maidana (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: isogeny class; class of matrices; group of rational points; cyclic; ordinary abelian variety; finite field

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Alejandro J. Giangreco-Maidana. Cyclic abelian varieties over finite fields in ordinary isogeny classes. Mathematical Communications, 2021, 26 (2), pp.151-158. ⟨hal-02528812⟩