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Central Simple Algebras and Galois Cohomology
Philippe GilleTamás Szamuely
出版Cambridge University Press, 2017-08-10
主題Mathematics / Algebra / GeneralMathematics / AppliedMathematics / Geometry / GeneralMathematics / Topology
ISBN11071563789781107156371
URLhttp://books.google.com.hk/books?id=CpsqDwAAQBAJ&hl=&source=gbs_api
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註釋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.