Local Fields by Jean-Pierre Serre (English) Hardcover Book

Description: Local Fields by Jean-Pierre Serre, Marvin J. Greenberg The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray. Table of Contents One Local Fields (Basic Facts).- I Discrete Valuation Rings and Dedekind Domains.- II Completion.- Two Ramification.- III Discriminant and Different.- IV Ramification Groups.- V The Norm.- VI Artin Representation.- Three Group Cohomology.- VII Basic Facts.- VIII Cohomology of Finite Groups.- IX Theorems of Tate and Nakayama.- X Galois Cohomology.- XI Class Formations.- Four Local Class Field Theory.- XII Brauer Group of a Local Field.- XIII Local Class Field Theory.- XIV Local Symbols and Existence Theorem.- XV Ramification.- Supplementary Bibliography for the English Edition. Long Description The goal of this book is to present local class field theory from the cohomo Details ISBN0387904247 Author Marvin J. Greenberg Short Title LOCAL FIELDS 2/E Series Graduate Texts in Mathematics Language English ISBN-10 0387904247 ISBN-13 9780387904245 Media Book Format Hardcover Series Number 67 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States Translator Marvin J. Greenberg Illustrations 62 Illustrations, black and white; VIII, 241 p. 62 illus. DOI 10.1007/b90663;10.1007/978-1-4757-5673-9 AU Release Date 1995-07-14 NZ Release Date 1995-07-14 UK Release Date 1995-07-14 Pages 241 Publisher Springer-Verlag New York Inc. Edition Description 1st ed. 1979. Corr. 2nd printing 1995 Edition 1st Alternative 9781475756753 DEWEY 512.3 Audience Undergraduate Year 1980 Publication Date 1980-01-19 US Release Date 1980-01-19 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96253553;

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