Marseglia, Stefano;
Springer, Caleb;
(2023)
Every finite abelian group is the group of rational points of an ordinary abelian variety over F2, F3 and F5.
Proceedings of the American Mathematical Society
, 151
(2)
pp. 501-510.
10.1090/proc/16127.
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Abstract
We show that every finite abelian group occurs as the group of rational points of an ordinary abelian variety over F2, F3 and F5. We produce partial results for abelian varieties over a general finite field Fq. In particular, we show that certain abelian groups cannot occur as groups of rational points of abelian varieties over Fq when q is large. Finally, we show that every finite cyclic group arises as the group of rational points of infinitely many simple abelian varieties over F2
| Type: | Article |
|---|---|
| Title: | Every finite abelian group is the group of rational points of an ordinary abelian variety over F2, F3 and F5 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/proc/16127 |
| Publisher version: | https://doi.org/10.1090/proc/16127 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10180997 |
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