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Galois Module Structure : Fields Institute Monographs - Victor P. Snaith

Galois Module Structure

Fields Institute Monographs

Hardcover Published: January 1994
ISBN: 9780821802649
Number Of Pages: 207

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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 id\'elic-valued functions on the complex representations of $G$. Following a theme pioneered by A. Frölich, 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 $s = -1$.

Basic Preliminariesp. 1
Class-Groupsp. 37
Logarithmic Techniquesp. 65
The Tame Casep. 101
Maximal Ordersp. 113
Quaternionic Examplesp. 135
Higher Algebraic K-Theoryp. 183
Indexp. 200
Bibliographyp. 205
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780821802649
ISBN-10: 082180264X
Series: Fields Institute Monographs
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 207
Published: January 1994
Publisher: American Mathematical Society
Country of Publication: US
Dimensions (cm): 26.67 x 18.42  x 1.91
Weight (kg): 0.57

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