Mixed motives over k[t]/(t^m+1)

Abstract

For a perfect field k, we use the techniques of Bondal-Kapranov and Hanamura to construct a tensor triangulated category of mixed motives over the truncated polynomial ring k[t]/(t^m+1). The extension groups in this category are given by Bloch's higher Chow groups and the additive higher Chow groups. The main new ingredient is the moving lemma for additive higher Chow groups by the authors and its refinements.