This article mentions singular curves having trivial Brauer group. Can we use coverings by such curves, together with descent, to get a handle on Brauer groups of other curves? [arXiv:1212.6019] Singular curves and the etale Brauer-Manin obstruction for surfaces from arXiv Front: math.NT by Yonatan Harpaz, Alexei Skorobogatov We construct a smooth and projective surface over an arbitrary number field that is a counterexample to the Hasse principle but has the infinite etale Brauer-Manin set. We also construct a surface with a unique rational point and the infinite etale Brauer-Manin set. The key new ingredient is the arithmetic of singular projective curves.
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