Local duality for structured ring spectra

Abstract

We use the abstract framework constructed in our earlier paper to study local duality for Noetherian ${\mathbb{E}}_{\infty }$-ring spectra. In particular, we compute the local cohomology of relative dualizing modules for finite morphisms of ring spectra, thereby generalizing the local duality theorem of Benson and Greenlees. We then explain how our results apply to the modular representation theory of compact Lie groups and finite group schemes, which recovers the theory previously developed by Benson, Iyengar, Krause, and Pevtsova.

Revised version, to appear in Journal of Pure and Applied Algebra

References in corpus (2)

• Higher Topos Theory
• Local duality in algebra and topology

Cited by in corpus (8)

• Local duality in algebra and topology
• Local duality for representations of finite group schemes
• The algebraic chromatic splitting conjecture for Noetherian ring spectra
• The homotopy limit problem and the cellular Picard group of Hermitian $K$-theory
• Local Gorenstein duality for cochains on spaces
• Stratifying integral representations of finite groups
• Rational local systems and connected finite loop spaces
• Local Gorenstein duality in chromatic group cohomology