Transcendental obstructions to weak approximation on general K3 surfaces
arXiv:1005.1879 · doi:10.1016/j.aim.2011.06.017
Abstract
We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental Brauer-Manin obstruction to weak approximation. To do so, we exploit the relationship between polarized K3 surfaces endowed with particular kinds of Brauer classes and cubic fourfolds.
24 pages, 3 figures, Magma scripts included at the end of the source file.