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arXiv · 1310.5055

Pathologies of the Brauer-Manin obstruction

Jean-Louis Colliot-Thélène·Ambrus Pál·Alexei N. Skorobogatov
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Abstract

We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the \'etale Brauer-Manin obstruction. We also give simple examples of threefolds with the same property that are families of 2-dimensional quadrics, and discuss some other examples and general properties of the Brauer-Manin obstruction.

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Jean-Louis Colliot-Thélène, Ambrus Pál, Alexei N. Skorobogatov. 2013-10-18. Pathologies of the Brauer-Manin obstruction. https://arxiv.org/abs/1310.5055

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