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摘要翻译：
本文定义了满足某些有限条件的态射格式的l-adic同调。该同调具有与Chow群相似的函子：正推、平拉、碱基变化、Cap-积等。特别是在奇异变体上，这种l-adic同调比经典l-adic上同调表现得更好。作为应用，我们给出了在有限上同调维数域上构造任意代数格式的圈映射的一种更简单的方法。我们证明了这些圈映射杀死了代数等价，并在局部自由束的Chern作用下进行了交换。
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英文标题：
《The \'Etale Homology and The Cycle Maps in Adic Coefficients》
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作者：
Ting Li
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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：
In this article, we define the l-adic homology for a morphism of schemes satisfying certain finiteness conditions. This homology has these functors similar to the Chow groups: proper push-forward, flat pull-back, base change, cap-product, etc. In particular on singular varieties, this kind of l-adic homology behaves much better that the classical l-adic cohomology. As an application, we give an much easier approach to construct the cycle maps for arbitrary algebraic schemes over fields of finite cohomology dimension. And we prove these cycle maps kill the algebraic equivalences and commute with the Chern action of locally free sheaves.
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PDF链接：
https://arxiv.org/pdf/0712.1712
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