Algebraic cycles and higher K-theory
Algebraic cycles and higher K-theory
复制标题
代数环和高等 K 理论
DOI：
10.1016/0001-8708(86)90081-2
复制
发表时间：
1986
影响因子：
1.7
通讯作者：
S. Bloch
中科院分区：
文献类型：
--
作者：
S. Bloch
代数概型X上凝聚层范畴与凝聚层范畴的关系（即域上有限型的概型）和X上的代数圈群可以用Baum，富尔顿和麦克弗森的Riemann-Roth定理表示（为了简单起见，我们假设X是等维的）。这里G，（X）是X上相干层的Grothendieck群[13]，gr;是指由G上的y-过滤定义的分级群，（X）（参见Kratzer [14]、Soult [20]），CH '（X）是由富尔顿[9]定义的余维i代数圈的Chow群。左同构是G_i（X）上存在I-结构的形式推论，而r的存在是BFM RR定理的中心主题。本文的主要目的是定义一个高阶Chow群CH*（X，n），n20的理论，从而得到同构
The relation between the category of coherent sheaves on an algebraic scheme X (ie, a scheme of finite type over a field) and the group of algebraic cycles on X can be expressed in terms of the Riemann-Roth theorem of Baum, Fulton and McPherson (for simplicity we assume X equidimensional).Here G,(X) is the Grothendieck group of coherent sheaves on X [13], gr; refers to the graded group defined by the y-filtration on G,(X)(cf. Kratzer [14], Soult [20]), and CH’(X) is the Chow group of codimension i algebraic cycles defined by Fulton [9]. The left-hand isomorphism is a formal consequence of the existence of a I-structure on G,(X) while the existence of r is the central theme of the BFM RR theorem. The main purpose of this paper is to define a theory of higher Chow groups CH*(X, n), n 2 0, so as to obtain isomorphisms