The Completely Decomposed Topology on Schemes and Associated Descent Spectral Sequences in Algebraic K-Theory
The Completely Decomposed Topology on Schemes and Associated Descent Spectral Sequences in Algebraic K-Theory
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代数K理论中格式的完全分解拓扑及相关下降谱序列
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
Yevsey A. Nisnevich
中科院分区：
文献类型：
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作者：
Yevsey A. Nisnevich
设X是有限Krull维的Noether格式。引入了X上的一种新的Grothendieck拓扑，称为完全分解拓扑，并发展了相应的上同调和同伦理论的形式。这种形式被应用于构造收敛到X的各种代数K-群或更一般谱的同伦群的某些下降(或局部到全局)谱序列。他们改进了著名的Brown-Gersten谱序列。
Let X be a noetherian scheme of finite Krull dimension. A new Grothendieck topology on X, called the completely decomposed topology, is introduced, and the formalism of the corresponding cohomology and homotopy theories is developed. This formalism is applied to construct certain descent (or local-to-global) spectral sequences convergent to various algebraic K-groups of X, or to the homotopy groups of more general spectra. They refine the well-known Brown-Gersten spectral sequences.