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oai:docta.ucm.es:20.500.14352/571972023-08-26T23:27:08Zcom_20.500.14352_14col_20.500.14352_15

Andradas Heranz, Carlos Recio, Tomás Sendra, J. Rafael 2023-06-20T16:50:27Z 2023-06-20T16:50:27Z 1999 https://hdl.handle.net/20.500.14352/57197 https://dl.acm.org/citation.cfm?id=309845 http://www.acm.org 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. eng restricted access Base field restriction techniques for parametric curves. journal article