EQUIVARIANT UNIVERSAL COEFFICIENT AND KÜNNETH SPECTRAL SEQUENCES

Abstract

This paper constructs hyper-homology spectral sequences of $\mathbb{Z}$-graded and $RO_{G}$-graded Mackey functors that compute $\mathrm{Ext}$ and $\mathrm{Tor}$ over $G$-equivariant $S$-algebras ($A_{\infty}$ ring spectra) for finite groups $G$. These specialize to universal coefficient and K\"unneth spectral sequences.