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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On rational points on conics


Author: R. E. Macrae
Journal: Proc. Amer. Math. Soc. 67 (1977), 38-40
MSC: Primary 14H45
DOI: https://doi.org/10.1090/S0002-9939-1977-0453750-2
MathSciNet review: 0453750
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Abstract: The purpose of this paper is to prove the following result: let K be a finitely, separably generated extension field of transcendence degree one and genus zero over the exact constant field k. Assume that K has no k-rational points. Let L be a subfield of K that contains k. Then L has a k-rational point if and only if $ [K:L]$ is even.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0453750-2
Article copyright: © Copyright 1977 American Mathematical Society