Abstract

Let be a global field and a finite solvable -group. Under certain hypotheses concerning the extension splitting , we show that the homogeneous space with a semi-simple simply connected -group has the weak approximation property. We use a more precise version of this result to prove the Hasse principle for homogeneous spaces under a semi-simple simply connected -group with finite solvable geometric stabilizer , under certain hypotheses concerning the -kernel (or -lien) defined by X.