## Cohomology and Support in Representation Theory

## Commutative algebra for modular representations of finite groups

### Srikanth Iyengar (Nebraska)

The goal of these lectures will be to describe a bridge between the modular representation theory of finite groups and modules over polynomial rings. This has given us new insights and results, and also alternative proofs of certain classical ones, concerning modular representations. There has also been an impact on commutative algebra, for it has lead to the discovery of some unexpected results and phenomenon in that field. I will attempt to convey these ideas, by giving fairly complete proofs of some representative results from both areas.
**Reference:** This series of lectures is based on the following articles:

- L. L. Avramov, R-O. Buchweitz, S. B. Iyengar, and C. Miller, Homology of perfect complexes, Adv. Math. 223 (2010) 1731--1781; Corrigendum Adv. Math. 225 (2010) 3576--3578
- L. L. Avramov and S. B. Iyengar, Cohomology over complete intersections via exterior algebras,
- Triangulated categories (Leeds, 2006), London Math. Soc. Lecture Note Ser. 375, Cambridge Univ. Press, Cambridge, 2010, 52--75.
- D. Benson, S. B. Iyengar, and H. Krause, Module categories for finite group algebras, Proceedings of ICRA XIV (Tokyo, 2010) Eur. Math. Soc. Series of Congress Reports, 2011, 55--84.
- D. Benson, S. B. Iyengar, and H. Krause, Stratifying modular representations of finite groups, Ann. of Math. 174 (2011) 1643--1684.
- J. F. Carlson and S. B. Iyengar, Thick subcategories of the bounded derived category of a finite group, preprint 2012.
- S. Iyengar, Modules and cohomology over group algebras. One commutative algebraist's prespective, Trends in commutative algebra (Berkeley, September 2002), MSRI Publ. Vol. 51, Cambridge Univ. Press, Cambridge, 2004; 51--86.

Links to arXiv versions of these papers are available from the lecturer's publication page.

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