Singular curves and the etale Brauer-Manin obstruction for surfaces
  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. 
Yonatan Harpaz and Alexei Skorobogatov
math.AG math.NT