@article{c381a75c56754b15993f8367a0711592,
title = "Reductions of abelian surfaces over global function fields",
abstract = "Let be a non-isotrivial ordinary abelian surface over a global function field of characteristic p > 0 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.",
keywords = "abelian surfaces, deformation theory, elliptic curves",
author = "Davesh Maulik and Shankar, {Ananth N.} and Yunqing Tang",
note = "Funding Information: We thank Johan de Jong, Keerthi Madapusi Pera, Arul Shankar, Salim Tayou, and Jacob Tsimerman for helpful discussions. D.M. is partially supported by NSF FRG grant DMS-1159265. A.N.S. is partially supported by the NSF grant DMS-2100436. Y.T. is partially supported by the NSF grant DMS-1801237. We would like to thank the anonymous referees for thorough readings and valuable suggestions which have greatly helped improve this paper. Funding Information: We thank Johan de Jong, Keerthi Madapusi Pera, Arul Shankar, Salim Tayou, and Jacob Tsimerman for helpful discussions. D.M. is partially supported by NSF FRG grant DMS-1159265. A.N.S. is partially supported by the NSF grant DMS-2100436. Y.T. is partially supported by the NSF grant DMS-1801237. We would like to thank the anonymous referees for thorough readings and valuable suggestions which have greatly helped improve this paper. Publisher Copyright: {\textcopyright} 2022 The Author(s).",
year = "2022",
month = apr,
day = "16",
doi = "10.1112/S0010437X22007473",
language = "English (US)",
volume = "158",
pages = "893--950",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",
number = "4",
}