Cyclotomic Fields I and II - Couverture souple

Lang, Serge

Couverture souple

ISBN 10 : 1461269725 ISBN 13 : 9781461269724

Editeur : Springer, 2012

Synopsis

Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. For a long period in the 20th century this aspect of Kummer's work seems to have been largely forgotten, except for a few papers, among which are those by Pollaczek [Po], Artin-Hasse [A-H] and Vandiver [Va]. In the mid 1950's, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt. Iwasawa viewed cyclotomic fields as being analogues for number fields of the constant field extensions of algebraic geometry, and wrote a great sequence of papers investigating towers of cyclotomic fields, and more generally, Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers. Leopoldt concentrated on a fixed cyclotomic field, and established various p-adic analogues of the classical complex analytic class number formulas. In particular, this led him to introduce, with Kubota, p-adic analogues of the complex L-functions attached to cyclotomic extensions of the rationals. Finally, in the late 1960's, Iwasawa [Iw 11] made the fundamental discovery that there was a close connection between his work on towers of cyclotomic fields and these p-adic L-functions of Leopoldt - Kubota.

A propos du livre

Présentation de l'éditeur

Combining the works previously published as Cyclotomic Fields, V. I & II, this book introduces these number fields, which are of great interest in classical number theory and other areas such as K-theory. Covers p-adic L-functions, Iwasawa theory, and more.

Présentation de l'éditeur

This book is a combined edition of the books previously published as Cyclotomic Fields, Vol. I and II. It continues to provide a basic introduction to the theory of these number fields, which are of great interest in classical number theory, as well as in

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 1461269725
• ISBN 13: 9781461269724
• Reliure: Broché
• Numéro d'édition: 2
• Nombre de pages: 460
• Coordonnées du fabricant: KINESIS; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; 22391; Allemagne