2026-06-29T08:01:11Zhttps://docta.ucm.es/rest/oai/request

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

Base field restriction techniques for parametric curves. Andradas Heranz, Carlos Recio, Tomás Sendra, J. Rafael 512.7 Computer Science Theory & Methods Mathematica Applied Mathematics Geometria algebraica 1201.01 Geometría Algebraica International Symposium on Symbolic and Algebraic Computation, JUL 29-31, 1999 Vancouver,Canada 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. DGES DGESIC ESPTINT-IV:"FRISCO" DGES Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:50:27Z 2023-06-20T16:50:27Z 1999 journal article https://hdl.handle.net/20.500.14352/57197 XXXX-XXXX eng PB 95-0354 IFD-97-0409 PB 95-0563 restricted access application/pdf Association for Computing Machinery