# Exceptional splitting of abelian surfaces over global function fields.

Ananth Shankar, MIT
Tuesday, November 13, 2018 - 11:00am to 12:00pm
PDL C-401

Let $A$ denote a non-constant ordinary abelian surface over a global function field (of characteristic p) with good reduction everywhere. Suppose that $A$ does not have real multiplication by any real quadratic field with discriminant a multiple of $p$. Then we prove that there are infinitely many places modulo which $A$ is isogenous to the product of two elliptic curves. This is joint work with Davesh Maulik and Yunqing Tang.

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