Singular curves and the etale Brauer-Manin obstruction for surfaces

Published 25 Dec 2012 in math.AG and math.NT | (1212.6019v2)

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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