# Brauer-Manin obstruction and Hasse principle

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!

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## 1 Answer

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.

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Thank you very much! –  Timo Keller Jan 6 '12 at 18:32