The good reduction of generalized Kummer surfaces in the non-supersingular case

Tianchen Zhao

The good reduction of generalized Kummer surfaces in the non-supersingular case

Number Theory 2026-08-06 v1 Algebraic Geometry

Authors: Tianchen Zhao

Abstract

In this article, we study the good reduction of generalized Kummer surfaces, which are K3 surfaces obtained as minimal resolutions of quotients of abelian surfaces by finite groups. In particular, we establish a criterion for good reduction when the abelian surface has non-supersingular reduction and the group is cyclic. This extends the result of Lazda and Skorobogatov on Kummer surfaces.

Keywords

good reduction generalized Kummer surface K3 surface abelian surface non-supersingular

Cite

@article{arxiv.2608.06323,
  title  = {The good reduction of generalized Kummer surfaces in the non-supersingular case},
  author = {Tianchen Zhao},
  journal= {arXiv preprint arXiv:2608.06323},
  year   = {2026}
}