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We show that transcendental elements of the Brauer group of an algebraicsurface can obstruct the Hasse principle. We construct a general K3 surface Xof degree 2 over Q, together with a two-torsion Brauer class A that isunramified at every finite prime, but ramifies at real points of X. Motivatedby Hodge theory, the pair (X,A) is constructed from a double cover of P^2 x P^2ramified over a hypersurface of bi-degree (2,2).

Failure of the Hasse principle on general K3 surfaces