%0 Journal Article
%A Andradas Heranz, Carlos
%A Recio, Tomás
%A Sendra, J. Rafael
%T Base field restriction techniques for parametric curves.
%D 1999
%U https://hdl.handle.net/20.500.14352/57197
%X 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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