Cohomological Obstruction to the Hasse Principle for Homogeneous Spaces

摘要

In (Bo2) we proved that for a homogeneous space of a connected group with211u001econnected or abelian stabilizer, the Brauer-Manin obstruction to the Hasse 211u001eprinciple is the only obstruction. This obstruction was not however computed. 211u001eHere we define an obstruction to the Hasse principle for homogeneous space in 211u001eterms of Galois hypercohomology. We prove that this obstruction is the only 211u001eobstruction to the Hasse principle. Then we prove that this obstruction up to 211u001esign is the Brauer-Manin obstruction.