Relative Projectivity and Ideals in Cohomology Rings Original Research Article

In this paper we explore one aspect of the relationship between group cohomology and representation theory. For a finite groupGand a fieldkin characteristicp>0, ideals in the cohomology ringH*(G, k) can sometimes be characterized by exact sequences ofkG-modules in much the same way that elements of ExtkGare classically represented by exact sequences. Furthermore the maps on the stable category which represent the exact sequences have functorial properties which mimic the structure of the ideas in the ring. The natural setting for this study is the relative homological algebra for the module category, relative to the subcategory generated by a single module using the tensor product operation.