Let be an effective Cartier divisor on a regular quasiprojective scheme of dimension over a field. For an integer , we construct a cycle class map from the higher Chow groups with modulus to the relative -groups in the category of pro-abelian groups. We show that this induces a proisomorphism between the additive higher Chow groups of relative -cycles and the reduced algebraic -groups of truncated polynomial rings over a regular semilocal ring which is essentially of finite type over a characteristic zero field.
"Zero-cycles with modulus and relative $K$-theory." Ann. K-Theory 5 (4) 757 - 819, 2020. https://doi.org/10.2140/akt.2020.5.757