Relative K-theory via 0-cycles in finite characteristic

Let R be a regular semilocal ring, essentially of finite type over an infinite perfect field of characteristic p > 0. We show that the known cycle class map from the Chow group of 0-cycles with modulus to the relative K-theory induces a pro isomorphism between the additive higher Chow groups of relative 0-cycles and the relative K-theory of truncated polynomial rings over R. This settles the problem of completely describing the relative K-theory of such rings via the cycle class map.

Automated summary

This study demonstrates that under certain conditions, the known cycle class map from the Chow group to relative K-theory can be described via a pro isomorphism between the additive higher Chow groups and relative K-theory of truncated polynomial rings. This helps fully describe the relative K-theory of such rings through the cycle class map.