Etale Homotopy of Simplicial Schemes.
Etale Homotopy of Simplicial Schemes.
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单纯方案的 Etale 同伦。
DOI：
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发表时间：
1982
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通讯作者：
E. Friedlander
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作者：
E. Friedlander
这本书提出了一个关于etale同伦理论的现状，这是一种由M.Artin和B.Mazur引入抽象代数几何的拓扑理论。Eric M.Friedlander介绍了他自己在代数拓扑学、有限Chvalley群和代数几何中的许多应用。特别有趣的是关于亚当斯猜想、有限域的K-理论和庞加莱对偶的讨论。由于这些应用需要对etale同伦理论的原始公式进行反复修改，因此作者提供了一种新的基础处理方法，它比以前的版本更普遍、更精确。这本书的目的之一是向拓扑学家和代数几何学家提供etale同伦理论的基本技术和结果，他们可以在自己的工作中应用该理论。为了这类未来的应用，作者引入了一些新的构造(函数复形、相对同调和上同调、广义上同调)，这些构造立即被证明适用于代数K-理论。
This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions. One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory.