Failure of the Hasse principle for Chatelet surfaces in characteristic 2

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.

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

Cited by in corpus (2)

• Higher dimensional analogues of Châtelet surfaces
• Curves over every global field violating the local-global principle