Cyclotomic Fields and Zeta Values / Edition 1

Cyclotomic Fields and Zeta Values / Edition 1

by John Coates, R. Sujatha
     
 

ISBN-10: 3642069592

ISBN-13: 9783642069598

Pub. Date: 11/23/2010

Publisher: Springer Berlin Heidelberg

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

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Overview

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.

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Product Details

ISBN-13:
9783642069598
Publisher:
Springer Berlin Heidelberg
Publication date:
11/23/2010
Series:
Springer Monographs in Mathematics Series
Edition description:
Softcover reprint of hardcover 1st ed. 2006
Pages:
116
Product dimensions:
6.14(w) x 9.21(h) x 0.27(d)

Table of Contents

Cyclotomic Fields.- Local Units.- Iwasawa Algebras and p-adic Measures.- Cyclotomic Units and Iwasawa's Theorem.- Euler Systems.- Main Conjecture.

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