Vol. 6, No. 4, 2021

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Relative $K\mkern-2mu$-theory via $0$-cycles in finite characteristic

Rahul Gupta and Amalendu Krishna

Vol. 6 (2021), No. 4, 673–712
DOI: 10.2140/akt.2021.6.673

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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algebraic cycles, additive Chow groups, relative $K\mkern-2mu$-theory
Mathematical Subject Classification
Primary: 14C25
Secondary: 19E08, 19E15
Received: 24 November 2020
Revised: 30 April 2021
Accepted: 19 May 2021
Published: 12 February 2022
Rahul Gupta
Fakultät für Mathematik
Universität Regensburg
Amalendu Krishna
Department of Mathematics
Indian Institute of Science