Local Fields and Their Extensions (Translations of Mathematical Monographs, Vol. 121)

Fesenko, I.b.

ISBN 10: 082183259X / ISBN 13: 9780821832592

Published by American Mathematical Society, 2002

About this Item

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

Bibliographic Details

• Title: Local Fields and Their Extensions (Translations of Mathematical Monographs, Vol. 121)
• Publisher: American Mathematical Society
• Publication Date: 2002
• Language: English
• ISBN 10: 082183259X
• ISBN 13: 9780821832592
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: New

About this title

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.

Review

Well written ... A big amount of exercises contribute to the attraction of this highly original book. --Zentralblatt MATH