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More precisely, let X be an algebraic variety over a number field k. The variety X is called a counter-example to the Hasse principle, if X has a kv-poinl for any completion kv ofk, but has no fc-points. Manin [Mal], [Ma2] proposed a general method of explaining obstructions to the Hasse principle with the use of the Brauer group of X. For a kvariety X such that X(kO) is nonempty for any place v of k, Manin's method gives an obstruction for X to have a Ä>point. For a class # of fc-varieties a natural question arises, whether the Brauer-Manin obstruction is the only one, i.e. is it true that if Xe % X(kv) 0 for any place v of k, and there is no Brauer-Manin obstruction, then X must have a fc-point.

The Brauer-Manin obstructions for homogeneous spaces with connected or abelian stabilizer.