Fixed point adjunctions for equivariant module spectra

TL;DR

This paper explores the relationships between fixed points and inflation in equivariant module spectra over ring spectra, providing numerous examples beyond the rational torus case, with implications for algebraic models.

Contribution

It introduces new fixed point adjunctions in equivariant module spectra, extending previous rational torus results to broader non-rational and non-torus contexts.

Findings

Examples based on geometric fixed points

Applications to the Eilenberg-Moore spectral sequence

Extension of adjunctions beyond rational cases

Abstract

We consider the Quillen adjunction between fixed points and inflation in the context of equivariant module spectra over equivariant ring spectra, and give numerous examples including some based on geometric fixed points and some on the Eilenberg-Moore spectral sequence. These results were originally presented as part of our equivalence between rational torus-equivariant spectra and an algebraic model in arXiv:1101.2511. However, the present results apply in many other interesting cases explored here, which are not rational and where the ambient group is not a torus. The material in arXiv:1101.2511v3 will be revised to refer to this paper.