Reductions of abelian surfaces over global function fields

[摘要] 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.

[学科分类] 数学（综合）

[关键词] abelian surfaces;elliptic curves;deformation theory;11G10;14G17;11H55