2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63623Let 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.Algebraic Geometry14G15, 14J20, 14M20 (primary) 14C15, 14G20 (secondary)text