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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
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.

References [Enhancements On Off] (What's this?)

  • [1] M. Eichler, Introduction to the theory of algebraic numbers and functions, Academic Press, New York, 1966. MR 0209258 (35:160)
  • [2] M. Fried, Brauer groups and Jacobians (preprint).
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  • [4] R. E. MacRae, On the two-sheeted coverings of conics by elliptic curves, Trans. Amer. Math. Soc. 211 (1975), 277-287. MR 0379509 (52:414)

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Article copyright: © Copyright 1977 American Mathematical Society

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