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FAILURE OF THE HASSE PRINCIPLE ON GENERAL K3 SURFACES

Author:
Hassett, Brendan  Varilly-Alvarado, Anthony  


Journal:
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU


Issue Date:
2013


Abstract(summary):

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 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 P-2 x P-2 ramified over a hypersurface of bidegree (2, 2) .


Page:
853---877


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