Mixed motives over \(k[t]/(t^{m+1})\) (Q2894445)

Let \(k\) be a perfect field. The authors conctruct a tensor triangulated category of mixed motives over the truncated polynomial ring \(k[t]/(t^{m+1})\). This category is expected by the authors to be an appriopriate extension of the category of mixed motives to the simplest types of non-reduced rings. The motivic cohomology given by the Ext-groups in this category are given by Bloch's higher Chow groups and the additive higher Chow groups. The main technical result of the paper is the moving lemma for additive higher Chow groups and its refinements. The complete construction of such a category would allow one to construct the motivic cohomology that compute the \(K\)-theory of vector bundles on singular varieties. The authors study the particular case of this problem concerning singular varieties which are the infinitesimal deformations of smooth varieties.