### Relative stable categories of finite groups

Algebra and Geometry Seminar

22nd November 2017, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

I'll discuss what I know about representations of finite groups over finite quotients of the ring of integers. In this situation there are two stable categories one can consider: the group algebra is self-injective so there is the garden-variety stable category, but we can also work with another stable category by killing representations which are projective relative to the coefficients. I'll explain how to decompose the relative stable category in terms of representations over the residue field, and how to relate the two stable categories. This is a report on joint work with Baland and Chirvasitu, with Baland, and some work with Balmer might creep in.

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