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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Which curves over $ {\bf Z}$ have points with coordinates in a discrete ordered ring?


Author: Lou van den Dries
Journal: Trans. Amer. Math. Soc. 264 (1981), 181-189
MSC: Primary 03C65; Secondary 03B25, 10N05
MathSciNet review: 597875
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0597875-5
PII: S 0002-9947(1981)0597875-5
Article copyright: © Copyright 1981 American Mathematical Society