Appears in collection : Rational Points on Fano and Similar Varieties

We study the structure of homoge- neous spaces of linear algebraic groups over perfect fields and prove a result reducing certain nice properties or conjectures about homogeneous spaces to the crucial case of homogeneous spaces of the special linear group with finite stabilizers. In partic- ular, one can apply this reduction to the Brauer-Manin obstruction to the Hasse principle and weak approximation for rational points or zero-cycles of degree one over number fields (as in a recent work by Harpaz and Wittenberg).

(joint work with Giancarlo Lucchini-Arteche)