Discrete G-Spectra and embeddings of module spectra

TL;DR

This paper investigates the structure of discrete G-spectra for profinite groups, exploring embeddings of module spectra and their relationship with homotopy fixed points, using both classical and quasi-categorical frameworks.

Contribution

It introduces an embedding of module spectra into discrete G-spectra and compares classical and quasi-categorical approaches, establishing their equivalence under certain conditions.

Findings

Embedding of module objects in spectra into discrete G-spectra analyzed

Relationship between embeddings and homotopy fixed points studied

Equivalence of classical and quasi-categorical embeddings shown in specific cases

Abstract

In this paper we study the category of discrete G-spectra for a profinite group G. We consider an embedding of module objects in spectra into a category of module objects in discrete G-spectra, and study the relationship between the embedding and the homotopy fixed points functor. We also consider an embedding of module objects in terms of quasi-categories, and show that the two formulations of embeddings are equivalent in some circumstances.