1999/01/31 by János Kollár
Mathematics · #math.AG
published as Ann. of Math. (2) 150 (1999), no. 1, 357-367 · 11 pages, published version
arxiv created 1999/07/01 · arxiv updated 2009/11/30
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.