The computation is based of the Honda-Tate theorem which states that isogeny classes of abelian varieties over finite fields are completely determined by the characteristic polynomial of their Frobenius automorphism acting on the first $\ell$-adic cohomology group. For a given dimension $g$ and base field of size $q$, a complete list of all Weil polynomials that do occur can be enumerated using a technique developed by Kedlaya [MR:2459990, arXiv:0608104]. In 2016, Dupuy, Kedlaya, Roe and Vincent improved upon Kedlaya's original code to generate these tables and the data they contain.
- Review status: beta
- Last edited by Andrew Sutherland on 2019-10-18 12:38:34