The spectral sequence relating algebraic K-theory to motivic cohomology
The spectral sequence relating algebraic K-theory to motivic cohomology
复制标题
将代数 K 理论与动机上同调联系起来的谱序列
DOI：
10.1016/s0012-9593(02)01109-6
复制
发表时间：
2002
影响因子：
1.9
通讯作者：
A. Suslin
中科院分区：
文献类型：
--
作者：
E. Friedlander;A. Suslin
本文从域F的动机上同调与F的代数K-理论之间的Bloch-Lichtenbaum精确偶出发，对F上的任意光滑概型X构造了一个谱序列，其E2项是X的动机上同调，其邻接点是X的Quillen K-理论。在这个谱序列上表现出一个乘法结构。谱序列是与一个谱塔相关联的序列，该谱塔是通过考虑X上相干层通过支撑的余维的过滤而确定的。
Beginning with the Bloch–Lichtenbaum exact couple relating the motivic cohomology of a field F to the algebraic K-theory of F, the authors construct a spectral sequence for any smooth scheme X over F whose E2 term is the motivic cohomology of X and whose abutment is the Quillen K-theory of X. A multiplicative structure is exhibited on this spectral sequence. The spectral sequence is that associated to a tower of spectra determined by consideration of the filtration of coherent sheaves on X by codimension of support.