000 -LEADER |
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03876nam a22004575i 4500 |
003 - CONTROL NUMBER IDENTIFIER |
control field |
OSt |
005 - DATE AND TIME OF LATEST TRANSACTION |
control field |
20140310151452.0 |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
fixed length control field |
cr nn 008mamaa |
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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111114s2012 sz | s |||| 0|eng d |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
International Standard Book Number |
9783034802604 |
|
978-3-0348-0260-4 |
050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
Classification number |
QA174-183 |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
Classification number |
512.2 |
Edition number |
23 |
264 #1 - |
-- |
Basel : |
-- |
Springer Basel, |
-- |
2012. |
912 ## - |
-- |
ZDB-2-SMA |
100 1# - MAIN ENTRY--PERSONAL NAME |
Personal name |
Benson, David J. |
Relator term |
author. |
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
Title |
Representations of Finite Groups: Local Cohomology and Support |
Medium |
[electronic resource] / |
Statement of responsibility, etc |
by David J. Benson, Srikanth Iyengar, Henning Krause. |
300 ## - PHYSICAL DESCRIPTION |
Extent |
X, 105p. |
Other physical details |
online resource. |
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
Title |
Oberwolfach Seminars ; |
Volume number/sequential designation |
43 |
505 0# - FORMATTED CONTENTS NOTE |
Formatted contents note |
Preface -- 1 Monday -- 1.1 Overview -- 1.2 Modules over group algebras -- 1.3 Triangulated categories -- 1.4 Exercises -- 2 Tuesday -- 2.1 Perfect complexes over commutative rings -- 2.2 Brown representability and localization -- 2.3 The stable module category of a finite group -- 2.4 Exercises -- 3 Wednesday -- 3.1 -- 3.2 Koszul objects and support -- 3.3 The homotopy category of injectives -- 3.4 Exercises -- 4 Thursday -- 4.1 Stratifying triangulated categories -- 4.2 Consequences of stratification -- 4.3 The Klein four group -- 4.4 Exercises -- 5 Friday -- 5.1 Localising subcategories of D(A) -- 5.2 Elementary abelian 2-groups -- 5.3 Stratification for arbitrary finite groups -- 5.4 Exercises -- A Support for modules over commutative rings -- Bibliography -- Index. |
520 ## - SUMMARY, ETC. |
Summary, etc |
The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
Topical term or geographic name as entry element |
Mathematics. |
|
Topical term or geographic name as entry element |
Algebra. |
|
Topical term or geographic name as entry element |
Group theory. |
|
Topical term or geographic name as entry element |
Mathematics. |
|
Topical term or geographic name as entry element |
Group Theory and Generalizations. |
|
Topical term or geographic name as entry element |
Commutative Rings and Algebras. |
|
Topical term or geographic name as entry element |
Associative Rings and Algebras. |
700 1# - ADDED ENTRY--PERSONAL NAME |
Personal name |
Iyengar, Srikanth. |
Relator term |
author. |
|
Personal name |
Krause, Henning. |
Relator term |
author. |
710 2# - ADDED ENTRY--CORPORATE NAME |
Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
773 0# - HOST ITEM ENTRY |
Title |
Springer eBooks |
776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
Display text |
Printed edition: |
International Standard Book Number |
9783034802598 |
856 40 - ELECTRONIC LOCATION AND ACCESS |
Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-0348-0260-4 |
942 ## - ADDED ENTRY ELEMENTS (KOHA) |
Source of classification or shelving scheme |
|
Item type |
E-Book |