Transcendental obstructions to weak approximation on general K3 surfaces
Algebraic Geometry
2015-03-17 v1 Number Theory
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.
Cite
@article{arxiv.1005.1879,
title = {Transcendental obstructions to weak approximation on general K3 surfaces},
author = {Brendan Hassett and Anthony Várilly-Alvarado and Patrick Varilly},
journal= {arXiv preprint arXiv:1005.1879},
year = {2015}
}
Comments
24 pages, 3 figures, Magma scripts included at the end of the source file.