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CHARACTERISTIC POLYNOMIALS OF SIMPLE ORDINARY ABELIAN VARIETIES OVER FINITE FIELDS

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry Abelian varieties and schemes

Published online by Cambridge University Press:  19 February 2021

LENNY JONES Open the ORCID record for LENNY JONES [Opens in a new window]
LENNY JONES*
Affiliation:
Professor Emeritus of Mathematics, Department of Mathematics, Shippensburg University, Shippensburg, PA 17257, USA
*
e-mail: lkjone@ship.edu
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Abstract

We provide an easy method for the construction of characteristic polynomials of simple ordinary abelian varieties ${{\mathcal A}}$ of dimension g over a finite field ${{\mathbb F}}_q$, when $q\ge 4$ and $2g=\rho ^{b-1}(\rho -1)$, for some prime $\rho \ge 5$ with $b\ge 1$. Moreover, we show that ${{\mathcal A}}$ is absolutely simple if $b=1$ and g is prime, but ${{\mathcal A}}$ is not absolutely simple for any prime $\rho \ge 5$ with $b>1$.

Keywords

simple ordinary abelian varietyabsolutely simple abelian varietyfinite fieldcharacteristic polynomial

MSC classification

Primary: 11G25: Varieties over finite and local fields
Secondary: 14G15: Finite ground fields 14K05: Algebraic theory

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 391 - 397
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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