I am looking for


1. varieties without $\mathbf{Q}$-rational points where the absence can be explained by the Brauer-Manin obstruction, but not by the absence of adelic points
2. varieties without $\mathbf{Q}$-rational points where the absence cannot be explained by the Brauer-Manin obstruction


Thank you in advance!



Brauer-Manin obstruction and Hasse principle
Everything you want (and a whole lot more) is here: A. N. Skorobogatov, Torsors and rational points. Cambridge Tracts in Mathematics, 144. Cambridge University Press, 2001.


