Which curves over $\textbf {Z}$ have points with coordinates in a discrete ordered ring?
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- by Lou van den Dries
- Trans. Amer. Math. Soc. 264 (1981), 181-189
- DOI: https://doi.org/10.1090/S0002-9947-1981-0597875-5
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Abstract:
A criterion is given for curves defined over ${\mathbf {Z}}$ to have an infinite point in a discrete ordered ring. Using this, one can decide effectively whether a given polynomial in ${\mathbf {Z}}[X,Y]$ has a zero in a model for the axioms of open induction. Riemann-Roch for curves over ${\mathbf {Q}}$ is the main tool used.References
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Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 264 (1981), 181-189
- MSC: Primary 03C65; Secondary 03B25, 10N05
- DOI: https://doi.org/10.1090/S0002-9947-1981-0597875-5
- MathSciNet review: 597875