Cyclotomic Fields and Zeta Values

  • J. Coates
  • R. Sujatha

Table of contents

  1. Front Matter
    Pages i-x
  2. Pages 1-12
  3. Pages 13-31
  4. Pages 72-87
  5. Pages 89-99
  6. Pages 101-109
  7. Back Matter
    Pages 111-114

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 (the most celebrated example being the conjecture of Birch and Swinnerton-Dyer for elliptic curves).

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 graduate students and non-experts in Iwasawa theory.


Arithmetic Iwasawa theory Lie algebra cyclotomic fields function geometry main conjecture number theory proof theorem

Authors and affiliations

  • J. Coates
    • 1
  • R. Sujatha
    • 2
  1. 1.Centre for Mathematical SciencesDPMMSCB3 0WBCambridgeEngland
  2. 2.School of MathematicsTata Institute of Fundamental Research400 005MumbaiIndia

Bibliographic information