Reductions of abelian surfaces over global function fields
Number Theory
2020-08-11 v2 Algebraic Geometry
Abstract
Let be a non-isotrivial ordinary abelian surface over a global function field with good reduction everywhere. Suppose that does not have real multiplication by any real quadratic field with discriminant a multiple of . We prove that there are infinitely many places modulo which is isogenous to the product of two elliptic curves.
Cite
@article{arxiv.1812.11679,
title = {Reductions of abelian surfaces over global function fields},
author = {Davesh Maulik and Ananth N. Shankar and Yunqing Tang},
journal= {arXiv preprint arXiv:1812.11679},
year = {2020}
}
Comments
The sections have been reorganized and some details have been added in order to improve the clarity of the exposition