In this paper we study super-isolated abelian varieties, that is, abelian varieties over finite fields whose isogeny class contains a single isomorphism class. The goal of this paper is to (1) characterize whether a product of super-isolated varieties is super-isolated, and (2) characterize which super-isolated abelian varieties admit principal polarizations, and how many up to polarized isomorphisms.

中文翻译：

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超孤立阿贝尔品种的乘积和极化

在本文中，我们研究了超孤立阿贝尔簇，即有限域上的阿贝尔簇，其同基因类包含一个同构类。本文的目标是（1）表征超孤立簇的乘积是否是超孤立的，以及（2）表征哪些超孤立阿贝尔簇允许主极化，以及有多少到极化同构。