On the Adams spectral sequence for R –modules

Abstract

We discuss the Adams Spectral Sequence for R-modules based on commutative localized regular quotient ring spectra over a commutative S -algebra R in the sense of Elmendorf, Kriz, Mandell, May and Strickland. The formulation of this spectral sequence is similar to the classical case and the calculation of its E2 -term involves the cohomology of certain ‘brave new Hopf algebroids’ E∗RE . In working out the details we resurrect Adams’ original approach to Universal Coefficient Spectral Sequences for modules over an R ring spectrum.