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Luca Pol: Postdoc day, Seminar 4: Local Gorenstein duality in chromatic group cohomology

Time: Fri 2022-01-14 15.50 - 16.20

Location: Zoom, meeting ID: 921 756 1880

Video link: https://kva-se.zoom.us/j/9217561880

Participating: Luca Pol (Universität Regensburg)

Abstract: Many algebraic definitions and constructions can be made in a derived or homotopy invariant setting and as such make sense for ring spectra. Dwyer–Greenlees–Iyengar (followed by Barthel–Heard–Valenzuela) showed that one can make sense of local Gorenstein duality for ring spectra. In this talk, I will show that cochain spectra \(C^*(BG;R)\) satisfy local Gorenstein duality surprisingly often, and explain some of the implications of this. When \(R=k\) is a field this recovers duality properties in modular representation theory conjectured by Benson and later proved by Benson–Greenlees. However, the result also applies to more exotic coefficients R such as Lubin–Tate theories, K-theory spectra or topological modular forms, showing that chromatic analogues of Benson’s conjecture also hold. This is joint work with Jordan Williamson.