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Proceedings of the American Mathematical Society

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


Author: Jodi Black
Journal: Proc. Amer. Math. Soc. 139 (2011), 4163-4171
MSC (2010): Primary 11E72; Secondary 11E57
DOI: https://doi.org/10.1090/S0002-9939-2011-10844-X
Published electronically: April 12, 2011
MathSciNet review: 2823061
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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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Additional Information

Jodi Black
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: jablack@emory.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10844-X
Received by editor(s): October 7, 2010
Published electronically: April 12, 2011
Additional Notes: The results in this work are from a doctoral dissertation in progress under the direction of R. Parimala, whom the author sincerely thanks for her guidance
Communicated by: Ken Ono
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.