Failure of the Hasse principle for Chatelet surfaces in characteristic 2

Details Failure of the Hasse principle for Chatelet surfaces in characteristic 2 Failure of the Hasse principle for Chatelet surfaces in characteristic 2

2009-02-20

arxiv.org/abs/0902.3644v2

Mathematics

Number Theory

5 pages. Changed the title, added Lemma 3.2, made small changes to the introduction

Scientific paper

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.

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