The chromatic splitting conjecture for Noetherian commutative ring spectra

Tobias Barthel, Drew Heard, Gabriel Valenzuela

Published 2016-08-12Version 1

We formulate a version of Hopkins' chromatic splitting conjecture for an arbitrary structured ring spectrum $R$, and prove it whenever $\pi_*R$ is Noetherian. Our approach relies on a novel decomposition of the local cohomology functors constructed previously by Benson, Iyengar, and Krause as well as a generalization of Brown--Comenetz duality. As an application, these results provide a new local-to-global principle in the modular representation theory of finite groups.