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

Benson, David J.

ISBN 10: 3034802595 / ISBN 13: 9783034802598

Verlag: Birkhäuser, 2011

Beschreibung

Bestandsnummer des Verkäufers 524005dd9097f609f9b33e6917869c0b

Bibliografische Details

• Titel: Representations of Finite Groups: Local Cohomology and Support (eng)
• Verlag: Birkhäuser
• Erscheinungsjahr: 2011
• Sprache: Englisch
• ISBN-10: 3034802595
• ISBN-13: 9783034802598
• Einband: Softcover
• Zustand: new
• Gewicht: 0,26 Kilogramm

Über diesen Titel

Inhaltsangabe

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.

Von der hinteren Coverseite

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.