Representations of Finite Groups: Local Cohomology and Support (Paperback)

David J. Benson

ISBN 10: 3034802595 / ISBN 13: 9783034802598

Edité par Springer Basel, Basel, 2011

A propos de cet article

Paperback. 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 Quillens 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

N° de réf. du vendeur 9783034802598

Détails bibliographiques

• Titre: Representations of Finite Groups: Local Cohomology and Support (Paperback)
• Éditeur: Springer Basel, Basel
• Date de parution: 2011
• Langue: anglais
• ISBN à 10 chiffres: 3034802595
• ISBN à 13 chiffres: 9783034802598
• Reliure: Paperback
• État de l'article: new

A propos de ce titre

Synopsis

This book presents the solution of a long-standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on commutative algebra, cohomology of groups and stable homotopy theory.

Présentation de l'éditeur

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.