Local Fields and Their Extensions - Couverture rigide

American Mathematical Society

Couverture rigide

ISBN 10 : 082183259X ISBN 13 : 9780821832592

Editeur : American Mathematical Society, 2002

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2002
• Langue: anglais
• ISBN 10: 082183259X
• ISBN 13: 9780821832592
• Reliure: Relié
• Numéro d'édition: 2
• Nombre de pages: 345
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible