Nice triples and the Grothendieck–Serre conjecture concerning principal G-bundles over reductive group schemes

Abstract

The main result of this article is to reduce a proof of the conjecture to a statement about principal bundles on affine line over a regular local scheme. This reduction is obtained via a theory of nice triples, which goes back to the ideas of Voevodsky. As an application, an unpublished result due to Gabber is proved.