  We show the surjectivity of a specialisation map on higher $(0,1)$-cycles for
a smooth projective scheme over an excellent henselian discrete valuation ring.
This gives evidence for a conjecture stated in an article of 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 specialisation map we study is
related to a finiteness conjecture for the $n$-torsion of $CH_0(X)$, where $X$
is a variety over a $p$-adic field.
