Conference abstracts

Session S12 - Group Theory

July 28, 15:00 ~ 15:25

## The relative stable category

### Jon Frederick Carlson

### University of Georgia, USA - jfc@math.uga.edu

Let $G$ be a finite group and $k$ an algebraically closed field of of characteristic $p > 0$. Let ${\mathcal H}$ be a collection of $p$-subgroups of G. We investigate the relative stable category ${\bf stmod}_{\mathcal H}(kG)$ of finitely generated modules modulo ${\mathcal H}$-projective modules. Triangles in this category correspond to ${\mathcal H}$-split sequences. Hence, compared to the ordinary stable category there are fewer triangles and more thick subcategories. Our interest is in the spectrum of this category and its relationship to the induction functor. Of particular note is that in some cases, the spectrum of the category is not Noetherian.