
TL;DR
This paper characterizes super-isolated abelian varieties over finite fields using algebraic integers and proves that only finitely many such varieties exist for each dimension greater than or equal to three.
Contribution
It provides a classification of super-isolated abelian varieties via the Honda-Tate theorem and establishes finiteness results for fixed dimensions.
Findings
Finitely many super-isolated abelian varieties exist for each dimension g ≥ 3.
Characterization of these varieties using algebraic integers.
Application of Honda-Tate theorem to classify super-isolated varieties.
Abstract
We call an abelian variety over a finite field super-isolated if its (-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 , there are finitely many such varieties.
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