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摘要翻译：
母题同伦范畴可以根据不同的拓扑结构和不同的基础范畴来定义。由于许多原因（主要是由于粘滞定理），由关于Nisnevich拓扑的光滑格式建立的motivic同伦范畴起着杰出的作用，但在某些情况下，非常希望能够使用所有格式而不是光滑格式。本文证明了在奇异性分解假设下，域上所有格式关于CDH-拓扑的不稳定模体同伦范畴几乎等价于同一域上光滑格式关于Nisnevich拓扑的不稳定模体同伦范畴。为此，我们证明了Noetherian格式范畴上的标准CD-拓扑，包括CDH-拓扑，满足一定的条件，从而允许我们对单纯束的同伦理论使用广义Brown-Gersten方法。
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英文标题：
《Unstable motivic homotopy categories in Nisnevich and cdh-topologies》
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作者：
Vladimir Voevodsky
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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 built out of smooth schemes with respect to the Nisnevich topology plays a distinguished role but in some cases it is very 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. In order to do it we show that the standard cd-topologies on the category of Noetherian schemes, including the cdh-topology, satisfy certain conditions which allows one to use the generalized version of the Brown-Gersten approach to the homotopy theory of simplicial sheaves.
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PDF链接：
https://arxiv.org/pdf/0805.4576
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