Pathologies of the Brauer-Manin obstruction

20 Sep 2015 · Colliot-Thélène Jean-Louis, Pál Ambrus, Skorobogatov Alexei N. ·

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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Pathologies of the Brauer-Manin obstruction

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