Insufficiency of the Brauer-Manin obstruction applied to étale covers

@article{Poonen2010InsufficiencyOT,
  title={Insufficiency of the Brauer-Manin obstruction applied to {\'e}tale covers},
  author={B. Poonen},
  journal={Annals of Mathematics},
  year={2010},
  volume={171},
  pages={2157-2169}
}
  • B. Poonen
  • Published 2010
  • Mathematics
  • Annals of Mathematics
Let k be any global field of characteristic not 2. We construct a k-variety X such that X(k) is empty, but for which the emptiness cannot be explained by the Brauer-Manin obstruction or even by the Brauer-Manin obstruction applied to finite etale covers. 
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