Abstract

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.

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