Singular homology and class field theory of varieties over finite fields
Singular homology and class field theory of varieties over finite fields
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有限域上簇的奇异同源性和类域论
DOI：
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发表时间：
2000
期刊：
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通讯作者：
Michael Spiess
中科院分区：
文献类型：
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作者：
Alexander Schmidt;Michael Spiess
在 20 世纪 80 年代，主要由于 K. Kato 和 S. Saito [KS2]，发现了对高维场的推广。阿贝尔扩展的描述是根据广义闲置类群给出的，其相当复杂的定义基于 Milnor K-滑轮。然而，如果人们将注意力限制在无分支的扩展上（相对于 k 的常规投影模型 X̄），那么类场论使用零循环模有理等价的 Chow 群 CH0(X̄) 具有很好的几何描述（参见 [KS1]、[Sa]）。
In the 1980s, mainly due to K. Kato and S. Saito [KS2], a generalization to higher dimensional fields has been found. The description of the abelian extensions is given in terms of a generalized idèle class group, whose rather involved definition is based on Milnor K-sheaves. However, if one restricts attention to unramified extensions (with respect to a regular, projective model X̄ of k), then class field theory has a nice geometric description using the Chow group CH0(X̄) of zero-cycles modulo rational equivalence (see [KS1], [Sa]).