Restriction isomorphism in arbitrary relative dimension

Prove that, for arbitrary relative dimension d, the restriction map from CH^{d+1}(X,1)_{\mathbb{Z}/p^r\mathbb{Z}} to the inverse limit of the Nisnevich cohomology groups H^d(X_k,\mathcal{K}^{M}_{X_n,d+1}/p^r) is an isomorphism.

Background

The paper defines a restriction map from the p^r-torsion higher Chow group CH^{d+1}(X,1) of a smooth projective model X over the ring of integers of a local field to the inverse limit of Milnor K-theory cohomology groups associated with the infinitesimal thickenings X_n of the special fiber.

For relative dimension two, the paper cites a theorem establishing that this map is an isomorphism, but the authors conjecture that the same assertion holds in every relative dimension. Such an extension would support the proposed description of the wild, p-primary part of higher-dimensional local class field theory.