GALOIS MODULE STRUCTURE (FIELDS INSTITUTE MONOGRAPHS) By Victor P. Snaith *VG+*

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ISBN-10
082180264X
Book Title
Galois Module Structure (Fields Institute Monographs)
ISBN
9780821802649
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
American Mathematical Society
ISBN-10
082180264X
ISBN-13
9780821802649
eBay Product ID (ePID)
8038826351

Product Key Features

Number of Pages
207 Pages
Language
English
Publication Name
Galois Module Structure
Publication Year
1994
Subject
Algebra / General
Type
Textbook
Subject Area
Mathematics
Author
American Mathem American Mathem
Series
Fields Institute Monographs
Format
Hardcover

Dimensions

Item Height
0.6 in
Item Weight
19.6 Oz
Item Length
9.8 in
Item Width
5.9 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
94-031144
Dewey Edition
20
Series Volume Number
2
Illustrated
Yes
Dewey Decimal
512/.74
Table Of Content
Basic preliminaries; Class-groups; Logarithmic techniques; The tame case; Maximal orders; Quaternionic examples; Higher algebraic $K$-theory; Index; Bibliography.
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 $s = -1$., 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 $s = -1$., Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. This title addresses the Chinburg conjectures. It provides the background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions., 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. A 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 Library of Explorers and Exploration Primary sources make these fascinating books unique. The titles in this visually stunning new biography series will provide middle school readers with an understanding of each explorer's life and achievements. Primary source documents such as journal entries, maps, and letters supplement engaging and detailed prose to explain the voyages and the impact they had on society and history. This series supports the social studies curriculum for: European exploration of the Americas; People, places and environment Samuel De Champlain - While many European explorers headed south in search of gold and spices, Samuel de Champlain spent his life in North America. He founded the first French colony at Quebec, traded with and fought with and against the local Native American tribes. He also mapped unknown territories such as Lake Huron and the lake in Vermont that bears his name, Lake Champlain.
LC Classification Number
QA247.S597 1994

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