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arXiv · 1009.4621

Zero Cycles of Degree One on Principal Homogeneous Spaces

Jodi Black
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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.

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Jodi Black. 2010-09-23. Zero Cycles of Degree One on Principal Homogeneous Spaces. https://arxiv.org/abs/1009.4621

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