Products and polarizations of super-isolated abelian varieties

Stefano Marseglia; Travis Scholl

doi:10.1007/s00209-021-02791-x

Products and polarizations of super-isolated abelian varieties

Stefano Marseglia, Travis Scholl

University of California at Irvine

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	445-462
Journal	Mathematische Zeitschrift
Volume	300
Early online date	22 Jun 2021
DOIs	https://doi.org/10.1007/s00209-021-02791-x
Publication status	Published - 2021

Bibliographical 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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Cite this

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author = "Stefano Marseglia and Travis Scholl",

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AU - Scholl, Travis

N1 - 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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Products and polarizations of super-isolated abelian varieties

Abstract

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