
Mathematics 2014
On GrothendieckSerre conjecture concerning principal Gbundles over regular semilocal domains containing a finite field: IIAbstract: In three preprints [Pan1], [Pan3] and the present one we prove GrothendieckSerre's conjecture concerning principal Gbundles over regular semilocal domains R containing a finite field (here $G$ is a reductive group scheme). The preprint [Pan1] contains main geometric presentation theorems which are necessary for that. The present preprint contains reduction of the GrothendieckSerre's conjecture to the case of semisimple simplyconnected group schemes (see Theorem 1.0.1). The preprint [Pan3] contains a proof of that conjecture for regular semilocal domains R containing a finite field. The GrothendieckSerre conjecture for the case of regular semilocal domains containing an infinite field is proven in joint work due to R.Fedorov and I.Panin (see [FP]). Thus the conjecture holds for regular semilocal domains containing a field. The reduction is based on two purity results (Theorem 1.0.2 and Theorem 10.0.29).
