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arXiv · 2209.00893

Non-invariance of weak approximation with Brauer-Manin obstruction for surfaces

Han Wu
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Abstract

In this paper, we study the property of weak approximation with Brauer-Manin obstruction for surfaces with respect to field extensions of number fields. For any nontrivial extension of number fields L/K, assuming a conjecture of M. Stoll, we construct a smooth, projective, and geometrically connected surface over K such that it satisfies weak approximation with Brauer-Manin obstruction off all archimedean places, while its base change to L fails. Then we illustrate this construction with an explicit unconditional example.

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Han Wu. 2022-09-02. Non-invariance of weak approximation with Brauer-Manin obstruction for surfaces. https://doi.org/10.4064/aa210827-19-8

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