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Abstract
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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.
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Keywords
algebraic cycles with modulus, relative algebraic
$K$-theory, additive higher Chow groups
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Mathematical Subject Classification 2010
Primary: 14C25
Secondary: 19E08, 19E15
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Milestones
Received: 8 January 2020
Revised: 23 April 2020
Accepted: 11 May 2020
Published: 26 December 2020
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