English

Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces

Number Theory 2021-09-07 v3 Algebraic Geometry

Abstract

A collection of varieties satisfies uniform potential density if each of them contains a dense subset of rational points after extending its ground field by a bounded degree. In this paper, we prove that uniform potential density holds for connected algebraic groups of a fixed dimension over fields of characteristic zero as well as elliptic K3 surfaces over number fields.

Keywords

Cite

@article{arxiv.2010.00563,
  title  = {Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces},
  author = {Kuan-Wen Lai and Masahiro Nakahara},
  journal= {arXiv preprint arXiv:2010.00563},
  year   = {2021}
}

Comments

Final version, accepted by International Mathematics Research Notices

R2 v1 2026-06-23T18:56:38.879Z