Abstract
We call an abelian variety over a finite field Fqsuper-isolated if its (Fq-rational) isogeny class contains a single isomorphism class. In this paper, we use the Honda-Tate theorem to characterize super-isolated ordinary simple abelian varieties by certain algebraic integers. Our main result is that for a fixed dimension g≥3, there are finitely many such varieties over all finite fields.
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