Insufficiency of the Brauer-Manin obstruction applied to étale covers

Abstract

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 étale covers.

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Authors

Bjorn Poonen

Massachusetts Institute of Technology
Department of Mathematics
77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States