A model for genuine equivariant commutative ring spectra away from the group order

TL;DR

This paper develops a framework for understanding genuine equivariant commutative ring spectra by leveraging geometric fixed points and Hill-Hopkins-Ravenel norms, especially when the group order is inverted, enabling more manageable computations.

Contribution

It introduces a novel approach using norm maps on geometric fixed point diagrams to analyze equivariant ring spectra away from the group order.

Findings

Provides a new computational method for equivariant spectra

Utilizes Hill-Hopkins-Ravenel norms in a novel way

Simplifies the homotopy theory analysis of equivariant spectra

Abstract

We use geometric fixed points to describe the homotopy theory of genuine equivariant commutative ring spectra after inverting the group order. The main innovation is the use of the extra structure provided by the Hill-Hopkins-Ravenel norms in the form of additional norm maps on geometric fixed point diagrams, which turns out to be computationally managable.