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

Local Gorenstein duality in chromatic group cohomology