Andradas Heranz, CarlosRecio, TomásSendra, J. Rafael2023-06-202023-06-201999https://hdl.handle.net/20.500.14352/57197International Symposium on Symbolic and Algebraic Computation, JUL 29-31, 1999 Vancouver,CanadaGiven 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.engjournal articlehttps://dl.acm.org/citation.cfm?id=309845http://www.acm.orgrestricted access512.7Computer ScienceTheory & MethodsMathematicaAppliedMathematicsGeometria algebraica1201.01 Geometría Algebraica