Motivic Cohomology

We present a program to prove the following conjecture: Let $S$ be the spectrum of a DVR of equi-characteristic zero with field of fraction $K$ and residue field $k$. The functor (associated to the choice of a uniformizing) $\Psi:DM_{gm}(K) \to DM_{gm}(k)$ is conservative (i.e. detects isomorphisms).