One construction of a K3 surface with a dense set of rational points

Ilya Karzhemanov

One construction of a K3 surface with a dense set of rational points

Algebraic Geometry 2015-09-08 v7 Number Theory

Authors: Ilya Karzhemanov

Abstract

We prove that there exists a number field $\fie$ and a smooth projective $\mathrm{K3}$ surface $S_{22}$ (of genus $12$ ) over $\fie$ such that the geometric Picard number of $S_{22}$ is equal to $1$ and the $\fie$ -rational points of $S_{22}$ are Zariski dense.

Keywords

K3 surface rational points Zariski dense Picard number number field genus 12

Cite

@article{arxiv.1102.1873,
  title  = {One construction of a K3 surface with a dense set of rational points},
  author = {Ilya Karzhemanov},
  journal= {arXiv preprint arXiv:1102.1873},
  year   = {2015}
}

Comments

17 pages; revised a lot and rewritten completely

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