Local Gorenstein duality in chromatic group cohomology

Abstract

We consider local Gorenstein duality for cochain spectra C⁎(BG;R) on the classifying spaces of compact Lie groups G over complex orientable ring spectra R. We show that it holds systematically for a large array of examples of ring spectra R, including Lubin-Tate theories, topological K-theory, and various forms of topological modular forms. We also prove a descent result for local Gorenstein duality which allows us to access further examples.