The algebraic chromatic splitting conjecture for Noetherian ring spectra

Abstract

We formulate a version of Hopkins' chromatic splitting conjecture for an arbitrary structured ring spectrum $R$, and prove it whenever ${\pi }_{\ast }R$ is Noetherian. As an application, these results provide a new local-to-global principle in the modular representation theory of finite groups.

Final version to appear in Mathematische Zeitschrift

References in corpus (3)

• Local duality in algebra and topology
• Local duality for structured ring spectra
• Affine weakly regular tensor triangulated categories

Cited by in corpus (2)

• Local Gorenstein duality for cochains on spaces
• From Ohkawa to strong generation via approximable triangulated categories -- a variation on the theme of Amnon Neeman's Nagoya lecture series