On a base change conjecture for higher zero-cycles

We show the surjectivity of a restriction map for higher (0, l)-cycles for a smooth projective scheme over an excellent henselian discrete valuation ring. This gives evidence for a conjecture by Kerz, Esnault and Wittenberg saying that base change holds for such schemes in general for motivic cohomology in degrees (i, d) for fixed d being the relative dimension over the base. Furthermore, the restriction map we study is related to a finiteness conjecture for the n-torsion of CH0(X), where X is a variety over a p-adic field