Characteristic Polynomials of Simple Ordinary Abelian Varieties over Finite Fields

2020/11/27 by Jones, Lenny
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2011.13708

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≥ 4 and 2g=ρ^b-1(ρ-1) for some prime ρ≥ 5, with b≥ 1. Moreover, we show that \mathcal A is absolutely simple if b=1 and ρ=5, but \mathcal A is not absolutely simple for arbitrary ρ with b>1.

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