Central Simple Algebras and Galois Cohomology: Contents
Central Simple Algebras and Galois Cohomology: Contents
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中心简单代数和伽罗瓦上同调：目录
DOI：
10.1017/cbo9780511607219
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发表时间：
2006
影响因子：
1.5
通讯作者：
Tam'as Szamuely
中科院分区：
文献类型：
--
作者：
P. Gille;Tam'as Szamuely
第一个全面的，现代的介绍理论的中心简单代数在任意领域，这本书从基础开始，并达到这样的先进成果的Merkurjev-Suslin定理，一个高潮的工作发起的布劳尔，诺特，哈塞和阿尔伯特和起点目前的研究动机上同调理论Voevodsky，Suslin，罗斯特和其他人。假设只有一个坚实的背景代数，文字涵盖了基本理论的中心简单代数，方法的伽罗瓦下降和伽罗瓦上同调，塞维里-布劳尔品种，技术在米尔诺尔K-理论和K-上同调，导致充分证明的Merkurjev-Suslin定理及其应用的特点减少规范。最后一章给出了正特征的结果，包括Bloch-Gabber-Kato定理和Izhboldin定理。这第二版已仔细修订和更新，并包含重要的附加主题。
The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi– Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev–Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch–Gabber–Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics.