Abelian varieties of prescribed order over finite fields

Raymond van Bommel, Edgar Costa, Wanlin Li +2

Given a prime power $q$ and $n\gg 1$, we prove that every integer in a large subinterval of the Hasse--Weil interval $[(\sqrt{q}-1{)}^{2n},(\sqrt{q}+1{)}^{2n}]$ is $#A(\mathbb{F}_q)$…