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

Jodi Black

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arXiv · 1010.1582

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

Jodi Black

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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.

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Jodi Black. 2010-10-08. Implications of the Hasse Principle for Zero Cycles of Degree One on Principal Homogeneous Spaces. https://arxiv.org/abs/1010.1582

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