Reductions of abelian surfaces over global function fields Article Swipe

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Davesh Maulik , Ananth N. Shankar , Yunqing Tang ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.1112/s0010437x22007473 · OA: W2907923887

Let $A$ be a non-isotrivial ordinary abelian surface over a global function field of characteristic $p>0$ 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.