Every finite abelian group is the group of rational points of an ordinary abelian variety over F2, F3 and F5

Stefano Marseglia, Caleb Springer

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We show that every finite abelian group occurs as the group of rational points of an ordinary abelian variety over F 2, F 3 and F 5. We produce partial results for abelian varieties over a general finite field F q. In particular, we show that certain abelian groups cannot occur as groups of rational points of abelian varieties over F q when q is large.

Original languageEnglish
Pages (from-to)501-510
Number of pages10
JournalProceedings of the American Mathematical Society
Volume151
Issue number2
DOIs
Publication statusPublished - Feb 2023

Bibliographical note

Publisher Copyright:
© 2022 American Mathematical Society.

Funding

Received by the editors August 30, 2021, and, in revised form, February 9, 2022, and April 29, 2022. 2020 Mathematics Subject Classification. Primary 14K15; Secondary 14G15, 11G10. Key words and phrases. Abelian variety, finite fields, group of rational points. The first author was supported by NWO grant VI.Veni.202.107. The second author was partially supported by National Science Foundation award CNS-2001470 and by the Additional Funding Programme for Mathematical Sciences, delivered by EPSRC (EP/V521917/1) and the Heilbronn Institute for Mathematical Research.

FundersFunder number
Heilbronn Institute for Mathematical Research
National Science FoundationCNS-2001470
Engineering and Physical Sciences Research CouncilEP/V521917/1
Nederlandse Organisatie voor Wetenschappelijk OnderzoekVI.Veni.202.107

    Keywords

    • Abelian variety
    • finite fields
    • group of rational points

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