The groups of points on abelian varieties over finite fields

Sergey Rybakov

Published 2009-03-02, updated 2010-06-30Version 4

Let $A$ be an abelian variety with commutative endomorphism algebra over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ without multiple roots. We give a classification of the groups of $k$-rational points on varieties from this class in terms of Newton polygons of $f_A(1-t)$.