English

Failure of the Hasse principle for Enriques surfaces

Number Theory 2011-03-29 v1 Algebraic Geometry

Abstract

We construct an Enriques surface X over Q with empty \'etale-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.

Keywords

Cite

@article{arxiv.1008.0596,
  title  = {Failure of the Hasse principle for Enriques surfaces},
  author = {Anthony Várilly-Alvarado and Bianca Viray},
  journal= {arXiv preprint arXiv:1008.0596},
  year   = {2011}
}

Comments

16 pages, 2 tables, Magma code included at the end of the source file