AG (Algebraic geometry)
Krishna and Levine: Additive higher Chow groups of schemes
arXiv:1001.5112 Mixed Motives over , by Amalendu Krishna, Jinhyun Park. For a perfect field , we construct a triangulated category of mixed motives over . The ext groups in this category are given by higher Chow groups, and additive higher Chow groups.
See the introduction to Additive Chow groups
nLab page on Additive higher Chow groups