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Synopsis
This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to Mathematical Reviews, 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor $K$-groups of fields and of local fields. The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's $p$-class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor $K$-groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas. The book is designed for graduate students and research mathematicians interested in local number theory and its applications in arithmetic algebraic geometry.
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Well written ... A big amount of exercises contribute to the attraction of this highly original book. --Zentralblatt MATH
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Local Fields and Their Extensions: A Constructive Approach (Translations of Mathematical Monographs)
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Local Fields and Their Extensions : A Constructive Approach
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Local Fields and Their Extensions A Constructive Approach
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Local Fields and Their Extensions
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Hardback. Condition: New. This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to ""Mathematical Reviews"", 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor $K$-groups of fields and of local fields.The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's $p$-class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor $K$-groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas. The book is designed for graduate students and research mathematicians interested in local number theory and its applications in arithmetic algebraic geometry. Seller Inventory # LU-9780821832592
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Local Fields and Their Extensions (Translations of Mathematical Monographs, Vol. 121)
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Local Fields and Their Extensions (Translations of Mathematical Monographs, Vol. 121)
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ISBN 10: 082183259X
ISBN 13: 9780821832592
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Condition: New. Offers an exposition of the arithmetical properties of local fields using constructive tools and methods. This book consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor $K$-groups of fields and of local fields. Series: Translations of Mathematical Monographs Reprint. Num Pages: 345 pages, Illustrations. BIC Classification: PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 230. Weight in Grams: 833. . 2002. 2nd Edition. Hardcover. . . . . Books ship from the US and Ireland. Seller Inventory # V9780821832592
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Local Fields and Their Extensions
Published by
American Mathematical Society, US, 2002
ISBN 10: 082183259X
ISBN 13: 9780821832592
New
Hardcover
Seller: Rarewaves.com UK, London, United Kingdom
Seller rating 5 out of 5 stars
Hardback. Condition: New. This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to ""Mathematical Reviews"", 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor $K$-groups of fields and of local fields.The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's $p$-class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor $K$-groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas. The book is designed for graduate students and research mathematicians interested in local number theory and its applications in arithmetic algebraic geometry. Seller Inventory # LU-9780821832592
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Local Fields and Their Extensions: A Constructive Approach (Translations of Mathematical Monographs) Vostokov S., V. und B. Fesenko I.
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Local Fields and Their Extensions (Translations of Mathematical Monographs, Vol. 121)
Published by
American Mathematical Society, 2002
ISBN 10: 082183259X
ISBN 13: 9780821832592
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Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, Ireland
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Condition: New. Offers an exposition of the arithmetical properties of local fields using constructive tools and methods. This book consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor $K$-groups of fields and of local fields. Series: Translations of Mathematical Monographs Reprint. Num Pages: 345 pages, Illustrations. BIC Classification: PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 230. Weight in Grams: 833. . 2002. 2nd Edition. Hardcover. . . . . Seller Inventory # V9780821832592
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