Failure of the Hasse principle on general K3 surfaces

Details Failure of the Hasse principle on general K3 surfaces Failure of the Hasse principle on general K3 surfaces

2011-10-08

arxiv.org/abs/1110.1738v1

Mathematics

Number Theory

LaTeX, 22 pages

Scientific paper

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).

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