Powers of abelian varieties over $\overline{\mathbb{Q}(t)}$ not isogenous to a Jacobian

Olivier de Gaay Fortman, Ananth N. Shankar

We prove the existence of abelian varieties over $\overline{\mathbb{Q}(t)}$ with no power isogenous to a Jacobian. Moreover, given a positive integer $N$, we prove the existence of…