Insufficiency of the Brauer-Manin obstruction applied to étale covers. (English) Zbl 1284.11096

Summary: 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.


11G35 Varieties over global fields
14G05 Rational points
14G25 Global ground fields in algebraic geometry
14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties
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