Fields Institute Monographs: Galois Module Structure

Snaith, Victor P.

ISBN 10: 082180264X / ISBN 13: 9780821802649

Published by American Mathematical Society, 1994

About this Item

This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,650grams, ISBN:9780821802649.

Seller Inventory # 8699673

Bibliographic Details

• Title: Fields Institute Monographs: Galois Module Structure
• Publisher: American Mathematical Society
• Publication Date: 1994
• Language: English
• ISBN 10: 082180264X
• ISBN 13: 9780821802649
• Binding: Hardcover
• Condition: Good
• Weight: 650 grams
• Seller catalogs:
  • Mathematics

About this title

Synopsis

Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. Typically these invariants lie in the class-group of some group-ring of $G$ or of a related order. These class-groups have ``Hom-descriptions'' in terms of idelic-valued functions on the complex representations of $G$. Following a theme pioneered by A. Frolich, T. Chinburg constructed several invariants whose Hom-descriptions are (conjecturally) given in terms of Artin root numbers. For a tame extension, the second Chinburg invariant is given by the ring of integers, and M. J. Taylor proved the conjecture in this case. The first published graduate course on the Chinburg conjectures, this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems. The final chapter introduces a new invariant constructed from algebraic $K$-theory, whose Hom-description is related to the $L$-function value at $s = -1$.

Review

It will be useful for specialists inside and outside of this subject, as well as for graduate students. --Zentralblatt für Mathematik