Pathologies of the Brauer-Manin obstruction
Algebraic Geometry
2015-09-22 v3 Number Theory
Abstract
We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the \'etale Brauer-Manin obstruction. We also give simple examples of threefolds with the same property that are families of 2-dimensional quadrics, and discuss some other examples and general properties of the Brauer-Manin obstruction.
Keywords
Cite
@article{arxiv.1310.5055,
title = {Pathologies of the Brauer-Manin obstruction},
author = {Jean-Louis Colliot-Thélène and Ambrus Pál and Alexei N. Skorobogatov},
journal= {arXiv preprint arXiv:1310.5055},
year = {2015}
}
Comments
22 pages, to appear in Mathematische Zeitschrift