%0 Journal Article
%T Failure of the Hasse principle on general K3 surfaces
%A Brendan Hassett
%A Anthony V¨¢rilly-Alvarado
%J Mathematics
%D 2011
%I arXiv
%X We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general K3 surface X of degree 2 over Q, together with a two-torsion Brauer class A that is unramified at every finite prime, but ramifies at real points of X. Motivated by Hodge theory, the pair (X,A) is constructed from a double cover of P^2 x P^2 ramified over a hypersurface of bi-degree (2,2).
%U http://arxiv.org/abs/1110.1738v1