Séminaires : Séminaire Variétés Rationnelles

We establish the Hasse principle and the weak approximation property for a family of homogeneous spaces of SLm whose geometric stabilizer is finite of nilpotency class 2, which were constructed by M. Borovoi and B. Kunyavskii. In particular, these homogeneous verify Colliot-Thélène's conjecture concerning Brauer-Manin obstruction for geometrically rationally connected varieties over number fields. The proof is by cohomological computation, the key argument an "arithmetic lemma" on a global property of Hilbert symbols, which is itself a consequence of Poitou-Tate duality.