Point counts of abelian varieties over finite fields determining their zeta function

Shiva Chidambaram, Timo Keller

Let $A$ be an abelian variety of dimension $g$ over a finite field ${\mathbf{F}}_q$. We show that if $q$ is sufficiently large relative to $g$, the $g$ point counts $\#A(\mathbf{F}_{…