Transcendental obstructions to weak approximation on general K3 surfaces

B Hassett, A Várilly-Alvarado, P Varilly - Advances in Mathematics, 2011 - Elsevier
Advances in Mathematics, 2011Elsevier
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.
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.
Elsevier
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