The algebraic chromatic splitting conjecture for Noetherian ring spectra
  We formulate a version of Hopkins' chromatic splitting conjecture for an arbitrary structured ring spectrum $R$, and prove it whenever $\pi_*R$ is Noetherian. As an application, these results provide a new local-to-global principle in the modular representation theory of finite groups. 
Tobias Barthel, Drew Heard, Gabriel Valenzuela
math.AT math.RT