@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",

}