Motivic cohomology of fat points in Milnor range via formal and rigid geometries

We present a formal scheme based cycle model for the motivic cohomology of fat points defined by truncated polynomial rings $$k[t]/(t^m)$$ with $$m \ge 2$$ , in one variable over field k. compute their Milnor range class groups when has sufficiently many elements. With some aids from rigid analytic geometry and Gersten conjecture K-theory resolved M. Kerz, we prove that resulting are isomorphic to K-groups rings, generalizing theorem Nesterenko-Suslin Totaro.