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arXiv · 2511.19410

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

Olivier de Gaay Fortman·Ananth N. Shankar
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Abstract

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 abelian varieties over $\overline{\mathbb Q(t)}$ with maximal monodromy such that the $n$th power is not isogenous to a Jacobian for $n \leq N$. We make use of an Arakelov inequality established by Lu and Zuo, as well as intersection theoretic methods, to prove our main results.

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Olivier de Gaay Fortman, Ananth N. Shankar. 2025-11-24. Powers of abelian varieties over $\overline{\mathbb Q(t)}$ not isogenous to a Jacobian. https://arxiv.org/abs/2511.19410

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