Geodesic
The characteristic polynomials of geometrically split ordinary abelian varieties of dimension $3$
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 12-16

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In the paper, we explicitly describe all possible characteristic polynomials of the Frobenius endomorphism for ordinary geometrically decomposable Abelian varieties of dimension $3$ over a finite field. These polynomials encode many arithmetic properties of abelian varieties including number of points. More precisely, if $\chi_{A,{q}}(T)$ is the characteristic polynomial of the Frobenius endomorphism on $A$ over $\mathbb{F}_q$, then the number of points on $A$ is equal to $\chi_{A,{q}}(1)$.
Keywords: Abelian threefold, characteristic polynomial, point-counting, finite field. 
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     author = {S. A. Novoselov},
     title = {The characteristic polynomials of geometrically split ordinary abelian varieties of dimension $3$},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {12--16},
     publisher = {mathdoc},
     number = {17},
     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/PDMA_2024_17_a2/}
}
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S. A. Novoselov. The characteristic polynomials of geometrically split ordinary abelian varieties of dimension $3$. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 12-16. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a2/