Implications of the Hasse Principle for Zero Cycles of Degree One on Principal Homogeneous Spaces

Jodi Black

paper

Implications of the Hasse Principle for Zero Cycles of Degree One on Principal Homogeneous Spaces

arXiv:1010.1582

Abstract

Let $k$ be a perfect field of virtual cohomological dimension $\leq 2$ . Let $G$ be a connected linear algebraic group over $k$ such that $G^{sc}$ satisfies a Hasse principle over $k$ . Let $X$ be a principal homogeneous space under $G$ over $k$ . We show that if $X$ admits a zero cycle of degree one, then $X$ has a $k$ -rational point.