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arXiv · 1212.6019

Singular curves and the etale Brauer-Manin obstruction for surfaces

Yonatan Harpaz·Alexei Skorobogatov
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Abstract

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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Yonatan Harpaz, Alexei Skorobogatov. 2013-11-22. Singular curves and the etale Brauer-Manin obstruction for surfaces. https://arxiv.org/abs/1212.6019

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