Vol. 5, No. 4, 2020

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Zero-cycles with modulus and relative $K$-theory

Rahul Gupta and Amalendu Krishna

Vol. 5 (2020), No. 4, 757–819
Abstract

Let D be an effective Cartier divisor on a regular quasiprojective scheme X of dimension d 1 over a field. For an integer n 0, we construct a cycle class map from the higher Chow groups with modulus {CHn+d(X|mD,n)}m1 to the relative K-groups {Kn(X,mD)}m1 in the category of pro-abelian groups. We show that this induces a proisomorphism between the additive higher Chow groups of relative 0-cycles and the reduced algebraic K-groups of truncated polynomial rings over a regular semilocal ring which is essentially of finite type over a characteristic zero field.

Keywords
algebraic cycles with modulus, relative algebraic $K$-theory, additive higher Chow groups
Mathematical Subject Classification 2010
Primary: 14C25
Secondary: 19E08, 19E15
Milestones
Received: 8 January 2020
Revised: 23 April 2020
Accepted: 11 May 2020
Published: 26 December 2020
Authors
Rahul Gupta
Fakultät für Mathematik
Universität Regensburg
Regensburg
Germany
Amalendu Krishna
School of Mathematics
Tata Institute of Fundamental Research
Mumbai
India