Categories of abelian varieties over finite fields I. Abelian varieties over ${\mathbb{F}}_p$

Tommaso Giorgio Centeleghe, Jakob Stix

We assign functorially a $\mathbb{Z}$-lattice with semisimple Frobenius action to each abelian variety over ${\mathbb{F}}_p$. This establishes an equivalence of categories that descr…