We construct spherical homogeneous spaces $X$ of semisimple simply connected groups with connected stabilizers such that the Hasse principle or weak approximation fail for $X$.
Referencias bibliográficas
M. Borovoi, On weak approximation in homogeneous spaces of simply connected algebraic groups, Proc. Int. Conf. “Automorphic Functions and...
M. Borovoi, The Hasse principle for homogeneous spaces, J. für die reine und angew. Math. 426 (1992), 179–192.
M. Borovoi, Abelian Galois cohomology of reductive groups, Mem. Amer. Math. Soc. (to appear).
M. Borovoi, The Brauer-Manin obstruction for homogeneous spaces with connected or abelian stabilizer, J. für die reine und angew. Math. 473...
J.-L. Colliot-Thélène et J.-J. Sansuc, La descente sur les variétés rationnelles, II, Duke Math. J. 54 (1987), 375–492.
G. Harder, Bericht über neuere Resultate der Galoiskohomologie halbeinfacher Matrizengruppen, Jahresbericht DMV 70 (1968), 182–216.
F. Knop, The Luna–Vust theory of spherical embeddings, Proc. Conf. “Algebraic groups and its applications, Hyderabad, 1989” (S. Ramanan, ed.),...
B. È. Kunyavskiĭ, Espaces homogènes sphériques: approximation faible et principe de Hasse, Séminaire de Théorie des Nombres de Paris 1991–92,...
A. S. Rapinchuk, The Hasse principle for symmetric spaces, Dokl. Akad. Nauk BSSR 31 (1987), 773–776. (Russian)
J.-J. Sansuc, Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres, J. für die reine und angew. Math....