Geometric Decomposition of Abelian Varieties of Order 1

Since the 1970s, the complete classification (up to isogeny) of abelian varieties over finite fields with trivial group of rational points has been known from results of Madan–Pal and Robinson; with two exceptions these are all defined over \(\mathbb {F}_2\) . We determine the decomposition of these varieties into simple factors over an algebraic closure of \(\mathbb {F}_2\) ; this requires solving a polynomial equation in three roots of unity.