Motivic cohomology of fat points in Milnor range

Abstract

We introduce a new algebraic-cycle model for the motivic cohomology theory of truncated polynomials k[t]/(tm) in one variable. This approach uses ideas from the deformation theory and non-archimedean analysis, and is distinct from the approaches via cycles with modulus. We prove that the groups in the Milnor range give the Milnor K-groups of k[t]/(tm), when the base field is of characteristic 0. Its relative part is the sum of the absolute Kähler differential forms.