The algebraic chromatic splitting conjecture for Noetherian ring spectra

TL;DR

This paper proves a version of Hopkins' chromatic splitting conjecture for structured ring spectra with Noetherian homotopy groups, leading to new insights in modular representation theory of finite groups.

Contribution

It formulates and proves a version of the chromatic splitting conjecture for Noetherian ring spectra, extending the conjecture's applicability.

Findings

Proves the conjecture for spectra with Noetherian homotopy groups.

Establishes a new local-to-global principle in modular representation theory.

Provides a framework connecting chromatic homotopy theory and representation theory.

Abstract

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.