Oberwolfach Seminar: Representations of Finite Groups: Local Cohomology and Support

Date

May 23rd - May 29th, 2010

Organizers

Dave Benson, Aberdeen

Srikanth Iyengar, Lincoln

Henning Krause, Paderborn

Programme

The seminar discusses some unifying themes in commutative algebra, representation theory, and homotopy theory. The underlying concept is the notion of support which provides a geometric approach for studying various algebraic structures. In terms of applications, the focus will be on modular representations of finite groups. In particular, classifications of thick and localizing subcategories of the stable module categories associated to a finite group will be presented.

There will be three series of lectures, starting with background material from group representation theory, commutative algebra, and the theory of derived categories. The goal is to explain local cohomology functors for specific triangulated categories and to discuss their applications.

Prerequisites

A solid background in algebra, including the basic theory of rings and modules, basic commutative algebra (first chapters of Atiyah/MacDonald), and basic homological algebra (derived functors, Ext, Tor).

Literature

The following books include basic material from representation theory, commutative algebra, and the theory of triangulated categories.

• J. Benson, Representations and cohomology of finite groups I,II, Cambridge University Press.
• W. Bruns and J. Herzog, Cohen-Macaulay rings, Cambridge University Press.
• R. Hartshorne, Local cohomology: A seminar given by A. Grothendieck (Harvard, 1961), Lecture Notes in Math. 41, Springer Verlag.
• A. Neeman, Triangulated categories, Princeteon University Press.

Deadline for applications

April 1st, 2010

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 25. The Institute covers accommodation and food. We are pleased that the Carl Friedrich von Siemens Foundation has decided to support the Oberwolfach Seminars from summer 2008 to summer 2013. By this support, travel expenses can be reimbursed up to 200 Euro in average per person. Participants can ask for travel support during their stay in Oberwolfach at the guest office against copy of travel receipts. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent preferably by e-mail (.ps or .pdf file) to:

    Prof. Dr. Dr. h.c. Gert-Martin Greuel
    Universität Kaiserslautern
    Fachbereich Mathematik
    Erwin Schrödingerstr.
    67663 Kaiserslautern, Germany