Two new motivic complexes for non-smooth schemes

These are expanded notes from a talk at the RIMS Workshop, Algebraic Number Theory and Related Topics, December 13th, 2023. We discussed Elmanto-Morrow's motivic complex, the procdh sheafification of the classical motivic complex, and their comparison. The procdh topology and the comparison is joint work with Shuji Saito. The comparison was obtained through joint discussion with Morrow, and its proof relies heavily on the main results of EM23.