K 3 surfaces over number fields with geometric Picard number one

@inproceedings{Ellenberg2003K3S,
  title={K 3 surfaces over number fields with geometric Picard number one},
  author={Jordan S. Ellenberg},
  year={2003}
}
A long-standing question in the theory of rational points of algebraic surfaces is whether a K3 surface X over a number field K acquires a Zariski-dense set of L-rational points over some finite extension L/K. In this case, we say X has potential density of rational points. In case XC has Picard rank greater than 1, Bogomolov and Tschinkel [2] have shown in many cases that X has potential density of rational points, using the existence of elliptic fibrations on X or large automorphism groups of… CONTINUE READING