Implications of the Hasse principle for zero cycles of degree one on principal homogeneous spaces

Black, Jodi

doi:10.1090/S0002-9939-2011-10844-X

Implications of the Hasse principle for zero cycles of degree one on principal homogeneous spaces
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by Jodi Black

Proc. Amer. Math. Soc. 139 (2011), 4163-4171

DOI: https://doi.org/10.1090/S0002-9939-2011-10844-X

Published electronically: April 12, 2011

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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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