Rigidity for relative 0-Cycles

We present a relation between the classical Chow group of relative 0-cycles on a regular scheme X , projective and flat over an excellent Henselian discrete valuation ring, and the Levine-Weibel Chow group of 0-cycles on the special fiber. We show that these two Chow groups are isomorphic with finite coefficients under extra assumptions. This generalizes a result of Esnault, Kerz and Wittenberg.