Commutative algebra for cohomology rings of classifying spaces of compact Lie groups (Q1373766)

Let \(G\) be a compact Lie group, \(BG\) its classifying space and \(k\) any field of coefficients. The authors apply some techniques of highly structured rings and module spectra to obtain a theorem for the cohomology ring \(H^*(BG;k)\). There exists a spectral sequence \(E_2^{s,t}=H_J^{s,t}(H^*(BG;k))\Rightarrow \widetilde H_{-s-t}(EG_+\wedge_GS^{\text{Ad}(G)};k)\) of modules over \(H^*(BG;k)\) with differentials \(d_r:E_r^{s,t}\rightarrow E_r^{s+r,t-r+1}\). In the oriented Cohen-Macaulay case, they obtain a functional equation for the Poincaré series.