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 language | English |
---|---|
Pages (from-to) | 501-510 |
Number of pages | 10 |
Journal | Proceedings of the American Mathematical Society |
Volume | 151 |
Issue number | 2 |
DOIs | |
Publication status | Published - 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.
Funders | Funder number |
---|---|
Heilbronn Institute for Mathematical Research | |
National Science Foundation | CNS-2001470 |
Engineering and Physical Sciences Research Council | EP/V521917/1 |
Nederlandse Organisatie voor Wetenschappelijk Onderzoek | VI.Veni.202.107 |
Keywords
- Abelian variety
- finite fields
- group of rational points