
School of Mathematics and Statistics
Jon Carlson
University of Georgia
The thick subcategory generated by the trivial module.
Friday 22nd January, 121pm, Carslaw 375.
We consider the stable category of $kG$modules modulo projectives,
where $G$ is a finite group and $k$ is a field of characteristic
$p > 0$. The thick subcategory $\Cal K$ generated by the trivial
module $k$ consists of all modules that can be pieced together by
extension from $k$ and from $\Omega^n(k)$ where $\Omega^n(k)$ is
the kernel of the $n^{th}$ boundary map in a complete resolution
of $k$. There is a sense in which all cohomology takes place in
$\Cal K$, and in the subcategory $\Cal K$ the module theory is
reasonably well behaved. The varieties defined by ordinary cohomology
measure the homological invariants of modules. A classification
of the thick subcategories of $\Cal K$ can be reasonably given.
Even the selfequivalences of $\Cal K$ can be characterized in a
nice way. In this lecture I will try to survey some of the recent
results in the area and present some examples to illustrate the
points.
