Reductions of abelian surfaces over global function fields

2018/12/31 by Maulik, Davesh, Shankar, Ananth N., Tang, Yunqing · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1812.11679

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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