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

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

2010-10-08

arxiv.org/abs/1010.1582v1

Mathematics

Number Theory

Scientific paper

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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