Cyclotomic Fields and Zeta Values

John Coates, R. Sujatha9783540330684, 3-540-33068-2

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 graduate students and non-experts in Iwasawa theory.

---

Table of contents :
front-matter……Page 1
1Cyclotomic Fields……Page 10
2Local Units……Page 22
3Iwasawa Algebras and p-adic Measures……Page 41
4Cyclotomic Units and Iwasawa’s Theorem……Page 54
5Euler Systems……Page 78
6Main Conjecture……Page 95
7Appendix……Page 106
back-matter……Page 115