Hassett, BrendanVarilly-Alvarado, Anthony2013-09-132013-09-132013Hassett, Brendan and Varilly-Alvarado, Anthony. "Failure of the Hasse Principle on General K3 Surfaces." <i>Journal of the Institute of Mathematics of Jessieu,</i> 12, no. 4 (2013) Oxford University Press: 853-877. http://dx.doi.org/10.1017/S1474748012000904.https://hdl.handle.net/1911/71906We 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 that is unramified at every finite prime, but ramifies at real points of X. Motivated by Hodge theory, the pair (X, ) is constructed from a double cover of P2 × P2 ramified over a hypersurface of bi-degree (2, 2).engThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Oxford University Press.Journal articlehttp://dx.doi.org/10.1017/S1474748012000904