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

Abstract

We prove that there exists a number field $\fie$ and a smooth projective $K3$ 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.

17 pages; revised a lot and rewritten completely

References in corpus (1)

• Birational geometry for number theorists