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Weak approximation and non-abelian fundamental groups. (English) Zbl 1073.14522

Summary: We introduce a new obstruction to weak approximation which is related to étale non-abelian coverings of a proper and smooth algebraic variety \(X\) defined over a number field \(k\). This enables us to give some counterexamples to weak approximation which are not accounted for by the Brauer–Manin obstruction, for example bielliptic surfaces.

MSC:

14G05 Rational points
11G35 Varieties over global fields
14F22 Brauer groups of schemes
14G25 Global ground fields in algebraic geometry
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