an:03983347
Zbl 0608.14004
Bloch, Spencer
Algebraic cycles and higher K-theory
EN
Adv. Math. 61, 267-304 (1986).
00152281
1986
j
14C35 14C40 18F25 14C05 14F05
higher Chow groups; Riemann-Roch theorem
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.
M.Stein