# Failure of the Hasse principle on general $K 3$ surfaces

@article{Hassett2013FailureOT,
title={Failure of the Hasse principle on general \$K 3\$ surfaces},
journal={Journal of the Institute of Mathematics of Jussieu},
year={2013},
volume={12},
pages={853 - 877}
}
• Published 2013
• Mathematics
• Journal of the Institute of Mathematics of Jussieu
Abstract We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general $K 3$ surface $X$ of degree $2$ over $\mathbb{Q}$, together with a 2-torsion Brauer class $\alpha$ that is unramified at every finite prime, but ramifies at real points of $X$. With motivation from Hodge theory, the pair $(X, \alpha )$ is constructed from a double cover of ${ \mathbb{P} }^{2} \times { \mathbb{P} }^{2}$ ramified over a… Expand
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