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2020 Zero-cycles with modulus and relative $K$-theory
Rahul Gupta, Amalendu Krishna
Ann. K-Theory 5(4): 757-819 (2020). DOI: 10.2140/akt.2020.5.757

Abstract

Let D be an effective Cartier divisor on a regular quasiprojective scheme X of dimension d1 over a field. For an integer n0, 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.

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Rahul Gupta. Amalendu Krishna. "Zero-cycles with modulus and relative $K$-theory." Ann. K-Theory 5 (4) 757 - 819, 2020. https://doi.org/10.2140/akt.2020.5.757

Information

Received: 8 January 2020; Revised: 23 April 2020; Accepted: 11 May 2020; Published: 2020
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.2140/akt.2020.5.757

Subjects:
Primary: 14C25
Secondary: 19E08, 19E15

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.5 • No. 4 • 2020
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