Failure of the Hasse principle on general K3 surfaces

Brendan Hassett; Anthony Várilly-Alvarado

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arXiv · 1110.1738

Failure of the Hasse principle on general K3 surfaces

Brendan Hassett·Anthony Várilly-Alvarado

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Abstract

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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Brendan Hassett, Anthony Várilly-Alvarado. 2011-10-08. Failure of the Hasse principle on general K3 surfaces. https://arxiv.org/abs/1110.1738

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