Failure of the Hasse principle for Enriques surfaces
arXiv:1008.0596 · doi:10.1016/j.aim.2010.12.020
Abstract
We construct an Enriques surface X over Q with empty étale-Brauer set (and hence no rational points) for which there is no algebraic Brauer-Manin obstruction to the Hasse principle. In addition, if there is a transcendental obstruction on X, then we obtain a K3 surface that has a transcendental obstruction to the Hasse principle.
16 pages, 2 tables, Magma code included at the end of the source file