R-equivalence on low degree complete intersections

Let k be a function field in one variable over C or the field C((t)). Let X be a k-rationally simply connected variety defined over k. In this paper we show that R-equivalence on rational points of X is trivial and that the Chow group of zero-cycles of degree zero A ₀(X) is zero. In particular, this holds for a smooth complete intersection of r hypersurfaces in P _k ⁿ of respective degrees (equation required).