  Let 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.
