2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77928Let X be a smooth, projective variety defined over a local field K. Following Manin, two K-points of X are called R-equivalent if they can be joined by a rational curve defined over K. The main result of this note shows that if there are only finitely many R-equivalence classes over the algebraic closure of K then the same holds over K. This also yields the unirationality of several classes of varieties over K.11 pages, published versionAlgebraic Geometrytext