R-equivalence and A¹-connectedness in anisotropic groups

الأصل · EN

We show that if G is an anisotropic, semisimple, absolutely almost simple, simply connected group over a field k, then two elements of G over any field extension of k are R-equivalent if and only if they are A¹-equivalent. As a consequence, we see that Sing*(G) cannot be A¹-local for such groups. This implies that the A¹-connected components of a semisimple, absolutely almost simple, simply connected group over a field k form a sheaf of abelian groups.