Transcendental obstructions to weak approximation on general K3 surfaces

Details Transcendental obstructions to weak approximation on general K3 surfaces Transcendental obstructions to weak approximation on general K3 surfaces

2010-05-11

arxiv.org/abs/1005.1879v1

Adv. Math., 228 (2011), 1377-1404

Mathematics

Algebraic Geometry

24 pages, 3 figures, Magma scripts included at the end of the source file.

Scientific paper

10.1016/j.aim.2011.06.017

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.

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