Failure of the Hasse principle on general K3 surfaces
Number Theory
2011-10-11 v1 Algebraic Geometry
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).
Keywords
Cite
@article{arxiv.1110.1738,
title = {Failure of the Hasse principle on general K3 surfaces},
author = {Brendan Hassett and Anthony Várilly-Alvarado},
journal= {arXiv preprint arXiv:1110.1738},
year = {2011}
}
Comments
LaTeX, 22 pages