Rationally connected varieties over finite fields

János Kollár, Endre Szabó

Published 2002-03-21, updated 2002-12-02Version 2

Let X be a geometrically rational (or more generally, separably rationally connected) variety over a finite field K. We prove that if K is large enough then X contains many rational curves defined over K. As a consequence we prove that R-equivalence is trivial on X if K is large enough. These imply that if Y is defined over a local field and it has good, separably rationally connected reduction then the Chow group of zero cycles is trivial for any residue field. R-equivalence is also trivial if the residue field is large enough.