${\mathbb{A}}^1$-connected components of classifying spaces and purity for torsors

Elden Elmanto, Girish Kulkarni, Matthias Wendt

In this paper, we study the Nisnevich sheafification ${\mathcal{H}}_{\acute{e}t}^1(G)$ of the presheaf associating to a smooth scheme the set of isomorphism classes of $G$-torsors, f…