Reductions of abelian surfaces over global function fields

Davesh Maulik; Ananth N. Shankar; Yunqing Tang

doi:10.1112/S0010437X22007473

Reductions of abelian surfaces over global function fields

Davesh Maulik, Ananth N. Shankar, Yunqing Tang

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	893-950
Number of pages	58
Journal	Compositio Mathematica
Volume	158
Issue number	4
DOIs	https://doi.org/10.1112/S0010437X22007473
State	Published - Apr 16 2022

Funding

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.

Keywords

abelian surfaces
deformation theory
elliptic curves

ASJC Scopus subject areas

Algebra and Number Theory

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10.1112/S0010437X22007473

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AU - Shankar, Ananth N.

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N2 - 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.

AB - 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.

KW - abelian surfaces

KW - deformation theory

KW - elliptic curves

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Reductions of abelian surfaces over global function fields

Abstract

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Keywords

ASJC Scopus subject areas

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