On rational points on conics
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- by R. E. Macrae PDF
- Proc. Amer. Math. Soc. 67 (1977), 38-40 Request permission
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
- Martin Eichler, Introduction to the theory of algebraic numbers and functions, Pure and Applied Mathematics, Vol. 23, Academic Press, New York-London, 1966. Translated from the German by George Striker. MR 0209258 M. Fried, Brauer groups and Jacobians (preprint). —, Poncelet correspondences, finite correspondences and Ritt’s theorem on commuting morphisms (preprint).
- R. E. MacRae, On the two sheeted coverings of conics by elliptic curves, Trans. Amer. Math. Soc. 211 (1975), 277–287. MR 379509, DOI 10.1090/S0002-9947-1975-0379509-5
Additional Information
- © Copyright 1977 American Mathematical Society
- 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