Zero Cycles of Degree One on Principal Homogeneous Spaces

Abstract

Let $k$ be a field of characteristic different from 2. Let $G$ be a simply connected or adjoint semisimple algebraic $k$-group which does not contain a simple factor of type $E_8$ and such that every exceptional simple factor of type other than $G_2$ is quasisplit. We show that if a principal homogeneous space under $G$ over $k$ admits a zero cycle of degree 1 then it has a $k$-rational point.