Rational SO(2)-Equivariant Spectra

TL;DR

This paper establishes a simple algebraic model for rational SO(2)-equivariant spectra, enabling algebraic analysis of ring and module spectra with monoidal structures.

Contribution

It provides the first comprehensive algebraic model for rational SO(2)-equivariant spectra, preserving monoidal properties for studying ring and module spectra.

Findings

Category of rational SO(2)-spectra has a simple algebraic model

Model categories and Quillen equivalences are monoidal

Facilitates algebraic understanding of ring and module spectra

Abstract

We prove that the category of rational SO(2)-equivariant spectra has a simple algebraic model. Furthermore, all of our model categories and Quillen equivalences are monoidal, so we can use this classification to understand ring spectra and module spectra via the algebraic model.