Products and polarizations of super-isolated abelian varieties

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Products and polarizations of super-isolated abelian varieties
 
Marseglia, Stefano; Scholl, Travis
(2021) Mathematische Zeitschrift, volume 300, pp. 445 - 462
(Article)
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, ... read more
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Keywords: General Mathematics
DOI: https://doi.org/10.1007/s00209-021-02791-x
ISSN: 0025-5874
Publisher: Springer
Note: Funding Information: The first author was partially supported by the Max Planck Society (Postdoctoral Fellowship) and by the Dutch Research Council (NWO grant 613.001.651). The second author was partially supported by Alfred P. Sloan Foundation (grant number G-2014-13575). The second author would also like to thank Alice Silverberg and Karl Rubin for helpful discussions on abelian varieties and class field theory. The authors thank Jonas Bergström, Valentijn Karemaker, Christophe Ritzenthaler and Shahed Sharif for comments, and Everett Howe helpful discussion that lead to the results contained in Sect. . The authors are grateful to the anonymous reviewer for helpful suggestions and comments. Publisher Copyright: © 2021, The Author(s).
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