Grothendieck - Serre Conjecture

We will continue with the proof of Grothendieck-Serre conjecture. The plan is to prove the following intermediate step: if G is a linear complex algebraic group and E is a G-torsor over A^1 x X, where X is a complex variety such that E is trivial on the complement of Z, where Z is a closed subscheme of A^1 x X finite over X, then for every point x of X there is a Zariski open neighborhood U of x in X such that E is trivial over A^1 x U. Along the way I will introduce and important gluing technique.