Unstable motivic homotopy categories in Nisnevich and cdh-topologies
Unstable motivic homotopy categories in Nisnevich and cdh-topologies
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Nisnevich 和 cdh 拓扑中的不稳定动机同伦类别
DOI：
10.1016/j.jpaa.2009.11.005
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发表时间：
2008
影响因子：
0.8
通讯作者：
V. Voevodsky
中科院分区：
文献类型：
--
作者：
V. Voevodsky
动机同伦范畴可以根据不同的拓扑和不同的基本范畴来定义。由于许多原因（主要是因为胶合定理），关于Nisnevich拓扑的光滑方案的运动同伦范畴起着杰出的作用，但在某些情况下，希望能够与所有方案一起工作，而不是光滑方案。本文证明了在奇点分解假设下，域上所有格式关于cdh-拓扑的不稳定运动同伦范畴几乎等价于同一域上光滑格式关于Nisnevich拓扑的不稳定运动同伦范畴.
The motivic homotopy categories can be defined with respect to different topologies and different underlying categories of schemes. For a number of reasons (mainly because of the Gluing Theorem) the motivic homotopy category of smooth schemes with respect to the Nisnevich topology plays a distinguished role but in some cases it is desirable to be able to work with all schemes instead of the smooth ones. In this paper we prove that, under the resolution of singularities assumption, the unstable motivic homotopy category of all schemes over a field with respect to the cdh-topology is almost equivalent to the unstable motivic homotopy category of smooth schemes over the same field with respect to the Nisnevich topology.