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arXiv · 2008.05738

Products and Polarizations of Super-Isolated Abelian Varieties

Stefano Marseglia·Travis Scholl
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Abstract

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.

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Stefano Marseglia, Travis Scholl. 2020-08-13. Products and Polarizations of Super-Isolated Abelian Varieties. https://doi.org/10.1007/s00209-021-02791-x

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