Additive cycle complex and coherent duality

Let k be a field of positive characteristic p, and X be a separated of finite type k-scheme of dimension d. We construct a cycle map from the additive cycle complex to the residual complex of Serre-Grothendieck coherent duality theory. This map is compatible with a cubical version of the map constructed in [Ren23] arXiv:2104.09662 when k is perfect. As a corollary, we get injectivity statements for (additive) higher Chow groups as well as for motivic cohomology (with modulus) with Z/p coefficients when k is algebraically closed.