Local Gorenstein duality in chromatic group cohomology

Abstract

We consider local Gorenstein duality for cochain spectra $C^{\ast }(BG;R)$ 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.

v3: 27 pages, to appear in JPAA

References in corpus (5)

• Global homotopy theory
• Extensions of the Benson-Solomon fusion systems
• Local duality for structured ring spectra
• Invertible $K(2)$-Local $E$-Modules in $C_4$-Spectra
• Local Gorenstein duality for cochains on spaces