Paper detail

Sur le groupe de Chow de codimension deux des variétés sur les corps finis

Using the construction of Colliot-Thélène and Ojanguren, we exhibit an example of a smooth projective geometrically rational variety X defined over a finite field F_p with an algebraic closure \bar F_p and the absolute Galois group G, such that the group H^3_nr(X, Z/2) is nonzero and the map CH^2(X)\to CH^2(\bar X)^G is not surjective.