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Abstract
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Let
be a
regular semilocal ring, essentially of finite type over an infinite perfect field of characteristic
. We show
that the known cycle class map from the Chow group of 0-cycles with modulus to the relative
-theory induces
a pro-isomorphism between the additive higher Chow groups of relative 0-cycles and the relative
-theory of truncated
polynomial rings over
.
This settles the problem of completely describing the relative
-theory of
such rings via the cycle class map.
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Keywords
algebraic cycles, additive Chow groups, relative
$K\mkern-2mu$-theory
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Mathematical Subject Classification
Primary: 14C25
Secondary: 19E08, 19E15
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Milestones
Received: 24 November 2020
Revised: 30 April 2021
Accepted: 19 May 2021
Published: 12 February 2022
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