Torsors over the punctured affine line

Abstract

We provide a classification of G-torsors over the punctured affine line Spec (k[t ±1 ]) where G is a reductive algebraic group defined over a field k of good characteristic. Our classification is in terms of the Galois cohomology of the complete field k((t)) with values in G. Keywords: Linear algebraic group, group scheme, torsor, punctured affine line, non-abelian cohomology.