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CHARACTERISTIC POLYNOMIALS OF SIMPLE ORDINARY ABELIAN VARIETIES OVER FINITE FIELDS
Published online by Cambridge University Press: 19 February 2021
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
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 391 - 397
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
References
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