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arXiv · 1812.11679

Reductions of abelian surfaces over global function fields

Davesh Maulik·Ananth N. Shankar·Yunqing Tang
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Abstract

Let $A$ be a non-isotrivial ordinary abelian surface over a global function field with good reduction everywhere. Suppose that $A$ does not have real multiplication by any real quadratic field with discriminant a multiple of $p$. We prove that there are infinitely many places modulo which $A$ is isogenous to the product of two elliptic curves.

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Davesh Maulik, Ananth N. Shankar, Yunqing Tang. 2018-12-31. Reductions of abelian surfaces over global function fields. https://arxiv.org/abs/1812.11679

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