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Products and Polarizations of Super-Isolated Abelian Varieties

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arxiv 2008.05738 v2 pith:TASDD7DG submitted 2020-08-13 math.NT math.AG

classification math.NTmath.AG
keywords super-isolatedvarietiesabeliancharacterizeclasspolarizationsadmitcontains
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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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