Relative projectivity and ideals in cohomology

Abstract

In this section we investigate methods of representing ideals in cohomology by exact sequences. Parts of the section will appear in joint work with Wayne Wheeler [CW] and with Chuang Peng [CP]. The foundation for our investigation was laid in the results at the end of Sect. 6. The point is that we will characterize ideals in cohomology by the modules in _kG mo∂ whose cohomology the ideals annihilate. To make the investigation more meaningful we begin by quoting the theorem on finite generation of Evens and Venkov (see [E]). One of the main facts which we use is that the ideals in cohomology are finitely generated.