Organisers: Radha Kessar, Henning Krause, Ran Levi, Markus Linckelmann, Peter Symonds
Organisers: Greg Stevenson, Jan Stovicek, Ivo Dell'Ambrogio
The goal of the summer school will be to understand and prove the following result, due to Benson, Carlson and Rickard [1]: the thick tensor ideal subcategories of the stable module category of a finite group are classified by the specialization closed subsets of the projective variety associated to cohomology ring of the group. This foundational theorem establishes the theory of support varieties as a powerful and elegant link between group cohomology and group representations, via algebraic geometry.
For the proof we will follow a recent approach due to Carlson and Iyengar [2], which has the advantage of providing a more direct link with Hopkins' similar classification for the derived category of perfect complexes over a commutative noetherian ring. This new point of view will require us to explore in some depth other topics - important on their own - such as derived categories, dg-algebras and dg-modules, and complete intersection rings.
The school will be accessible to graduate students and postdocs. Each participant is expected to contribute a talk, or to help in preparing a talk (depending on the number of participants), and most of the preparation should be done before the beginning of the school. Prerequisites are: proficiency with basic homological algebra, group representations, modules over rings; some familiarity with commutative algebra, algebraic geometry, derived categories.
| [1] | , and , Thick subcategories of the stable module category, Fund. Math. 153 (1997). 59–80 |
| [2] | and , Thick subcategories of the bounded derived category of a finite group, arXiv:1201.6536. |