Generalized Etale Cohomology Theories
Generalized Etale Cohomology Theories
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广义 Etale 上同调理论
DOI：
10.1007/978-3-0348-0066-2
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发表时间：
2004
影响因子：
0.8
通讯作者：
J. Jardine
中科院分区：
文献类型：
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作者：
J. Jardine
广义上的上同调理论是一种理论，它可以用一个代数变量上的谱表来表示，类似于空间上的普通谱表示上同调理论的方式。例子包括上同调和k理论。本书对博特周期k理论的Thomason下降定理和Nisnevich下降定理给出了新的完整的证明。在此过程中，它揭示了谱束的同伦理论的大部分主要思想，特别是广义谱束的同伦理论。为了充分处理杯积结构，本文提出了n倍谱的稳定同伦理论，并将其提升到n倍谱的预束水平。这本书应该感兴趣的所有研究人员在相关领域的代数k理论工作。这里介绍的技术本质上是组合的，因此是代数的。传统的稳定同伦理论没有广泛的背景。
A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. In doing so, it exposes most of the major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular. The treatment includes, for the purpose of adequately dealing with cup product structures, a development of stable homotopy theory for n-fold spectra, which is then promoted to the level of presheaves of n-fold spectra. This book should be of interest to all researchers working in fields related to algebraic K-theory. The techniques presented here are essentially combinatorial, and hence algebraic. An extensive background in traditional stable homotopy theory is not assumed.