Description
Book SynopsisWritten by two leading workers in the field, this brief but 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.
From the reviews: "The text is written in a clear and attractive style, with enough explanation helping the reader orientate in the midst of technical details." --ZENTRALBLATT MATH
Trade ReviewFrom 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 have contributed 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)
Table of ContentsCyclotomic Fields.- Local Units.- Iwasawa Algebras and p-adic Measures.- Cyclotomic Units and Iwasawa's Theorem.- Euler Systems.- Main Conjecture.
