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CHARACTERISTIC POLYNOMIALS OF SIMPLE ORDINARY ABELIAN VARIETIES OVER FINITE FIELDS

Published online by Cambridge University Press:  19 February 2021

LENNY JONES*
Affiliation:
Professor Emeritus of Mathematics, Department of Mathematics, Shippensburg University, Shippensburg, PA17257, USA
*

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 $b>1$ .

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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CHARACTERISTIC POLYNOMIALS OF SIMPLE ORDINARY ABELIAN VARIETIES OVER FINITE FIELDS
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CHARACTERISTIC POLYNOMIALS OF SIMPLE ORDINARY ABELIAN VARIETIES OVER FINITE FIELDS
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