Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (7 chapters)
Keywords
About this book
Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the deepest and most beautiful theorem known about them. It is also the simplest example of a vast array of subsequent, unproven "main conjectures'' in modern arithmetic geometry involving the arithmetic behaviour of motives over p-adic Lie extensions of number fields. These main conjectures are concerned with what one might loosely call the exact formulae of number theory which conjecturally link the special values of zeta and L-functions to purely arithmetic expressions.
Written by two leading workers in the field, this short and elegant book presents in full detail the simplest proof of the "main conjecture'' for cyclotomic fields. Its motivation stems not only from the inherent beauty of the subject, but also from the wider arithmetic interest of these questions. The masterly exposition is intended to be accessible to both graduatestudents and non-experts in Iwasawa theory.
Reviews
From the reviews:
"The author’s aim in this book is to present a proof of the so-called Iwasawa Main Conjecture for the pth cyclotomic field … . The text is written in a clear and attractive style, with enough explanation helping the reader orientate in the midst of technical details. According to the authors, the book is intended for graduate students and the non-expert in Iwasawa theory. I think that also the expert may enjoy reading this kind of unified treatment of such a beautiful theme." (Tauno Metsänkylä, Zentralblatt MATH, Vol. 1100 (2), 2007)
"This book was written to present in full detail a complete proof of the so-called ‘Main Conjecture’ in the arithmetic theory of cyclotomic fields. … The book is intended for graduate students and the non-expert in Iwasawa theory; however, the expert will find this work a valuable source in the arithmetic theory of cyclotomic fields. The book is very pleasant to read and is written with enough detail … . The authors havecontributed in an important way to Iwasawa theory with this beautiful book." (Gabriel D. Villa-Salvador, Mathematical Reviews, Issue 2007 g)
“The aim of this monograph is to present a detailed proof of the Main Conjecture, described by the authors as ‘the deepest result we know about the arithmetic of cyclotomic fields’. … This beautiful book will enable non-experts to study a state-of-the-art proof of the Main Conjecture. Furthermore, it might be a source of inspiration for new generations of mathematicians trying to tackle one of the many similar relations conjectured to hold in arithmetic geometry.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 154 (1), May, 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Cyclotomic Fields and Zeta Values
Authors: J. Coates, R. Sujatha
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-540-33069-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Hardcover ISBN: 978-3-540-33068-4Published: 18 August 2006
Softcover ISBN: 978-3-642-06959-8Published: 22 November 2010
eBook ISBN: 978-3-540-33069-1Published: 03 October 2006
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: X, 116
Topics: Number Theory