Rationally connected varieties over finite fields

János Kollár

Abstract of talk for the UM/OSU Seminar

Let X be a rationally connected variety over a finite field F. Given two F-points of X, is there a rational curve in X (defined over F) passing through these two points?

The answer to this question (and its generalizations) solve some conjectures of Colliot-Thélène on R-equivalence and on the Chow group of zero cycles.

UM/OSU Seminar