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Base field restriction techniques for parametric curves.

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Andradas Heranz, Carlos and Recio, Tomás and Sendra, J. Rafael (1999) Base field restriction techniques for parametric curves. ISSAC 99: PROCEEDINGS OF THE 1999 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION . pp. 17-22.

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Official URL: https://dl.acm.org/citation.cfm?id=309845


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Abstract

Given a variety V, implicitly defined over an algebraic separable field extension k(alpha), A. Weil [5] developed a restriction technique (called by him a descente method),that associates to V a suitable k-variety W, such that many properties of V can be analyzed by merely looking at W, that is, by descending to the base field k. In this paper we present a parametric counterpart, for curves, of Weil's construction. As an application, we state some simple algorithmic criteria over the variety W that translate, for instance, the k-definability of a parametric curve V, or the existence of an infinite number of L-rational points in V.


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International Symposium on Symbolic and Algebraic Computation, JUL 29-31, 1999 Vancouver,Canada

Uncontrolled Keywords:Computer Science; Theory & Methods; Mathematica; Applied; Mathematics
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14931
Deposited On:20 Apr 2012 11:42
Last Modified:09 Aug 2018 07:52

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