Modules over motivic cohomology
Modules over motivic cohomology
复制标题
动机上同调上的模
DOI：
10.1016/j.aim.2008.05.013
复制
发表时间：
2008
影响因子：
1.7
通讯作者：
P. A. Østvær
中科院分区：
文献类型：
--
作者：
O. Röndigs;P. A. Østvær
对于特征为零的域，我们证明了表示动机上同调的动机环谱上的模的同伦范畴等价于Voevodsky的动机大范畴。证明利用一些高度结构化的模型motivic稳定同伦理论，motivic Spanier-Whitehead对偶，同伦理论的motivic函子和motivic空间的转移，从地面上介绍了本文。工作与合理的系数，我们推广的等价性领域的特征零到所有完美的领域，采用技术的变更和同伦纯度的motivic同伦理论。
For fields of characteristic zero, we show that the homotopy category of modules over the motivic ring spectrum representing motivic cohomology is equivalent to Voevodsky's big category of motives. The proof makes use of some highly structured models for motivic stable homotopy theory, motivic Spanier–Whitehead duality, the homotopy theories of motivic functors and of motivic spaces with transfers as introduced from ground up in this paper. Working with rational coefficients, we extend the equivalence for fields of characteristic zero to all perfect fields by employing the techniques of alterations and homotopy purity in motivic homotopy theory.