Algebraic cycles and higher K-theory
type: Item
instance of: scholarly article
title: Algebraic cycles and higher K-theory
zbMATH Open document ID: 0608.14004
DOI: 10.1016/0001-8708(86)90081-2
author: Spencer Bloch
published in: Advances in Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The main purpose of this paper is to lay the foundations of a theory of higher Chow groups, \(CH^*(X,n)\), \(n\geq 0\), where X is a quasi- projective scheme over a field k, in such a way as to generalize the Riemann-Roch theorem of Baum, Fulton and MacPherson and establish results which have been available for some time in higher algebraic K-theory. These Chow groups are defined as the homotopy groups of a simplicial complex of graded abelian groups associated to X, and this complex is conjectured to satisfy certain axioms of Beilinson and Lichtenbaum. Among the properties established herein for \(CH^*(X,n)\) are: \((1)\quad functoriality\) (covariant for proper maps, contravariant for flat maps); \((2)\quad \hom otopy\); \((3)\quad localization\); \((4)\quad local\) to global spectral sequence; \((5)\quad multiplicative\) structure; and \((6)\quad Chern\) classes.
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 14C40
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 3983347
zbMATH Keywords: higher Chow groups
zbMATH Keywords: Riemann-Roch theorem
reviewed by: Michael R. Stein
Wikidata QID: Q56432004
MaRDI profile type: Publication
full work available at URL: 0001-8708(86)90081-2
OpenAlex ID: W2053133405
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description: scientific article; zbMATH DE number 3983347