Failure of the Hasse principle for Chatelet surfaces in characteristic 2
Number Theory
2012-10-04 v2 Algebraic Geometry
Abstract
Given any global field k of characteristic 2, we construct a Chatelet surface over k which fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic 2, thereby showing that the etale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.
Keywords
Cite
@article{arxiv.0902.3644,
title = {Failure of the Hasse principle for Chatelet surfaces in characteristic 2},
author = {Bianca Viray},
journal= {arXiv preprint arXiv:0902.3644},
year = {2012}
}
Comments
5 pages. Changed the title, added Lemma 3.2, made small changes to the introduction