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.
arXiv comment16 pages, 2 tables, Magma code included at the end of the source file
References in corpus (6)
- Transcendental obstructions to weak approximation on general K3 surfaces
- Insufficiency of the Brauer-Manin obstruction applied to etale covers
- Transcendental Brauer-Manin obstruction on a pencil of elliptic curves
- Visualizing elements of Sha[3] in genus 2 jacobians
- Diagonal quartic surfaces and transcendental elements of the Brauer group
- Effectivity of Brauer-Manin obstructions on surfaces