Homotopy theory of modules over a commutative $S-algebra: some tools and examples

Baker, A. (2020) Homotopy theory of modules over a commutative $S-algebra: some tools and examples. arXiv, (Unpublished)

Abstract

Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allow the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These have categories of modules which are generalisations of the classical categories of spectra that correspond to modules over the sphere spectrum; passing to their derived or homotopy categories leads to new contexts in which homotopy theory can be explored. In this paper we describe some of the tools available for studying these `brave new homotopy theories' and demonstrate them by considering modules over the K-theory spectrum, closely related to Mahowald's theory of bo-resolutions. In a planned sequel we will apply these techniques to the much less familiar context of modules over the 2-local connective spectrum of topological modular forms.

• Item Type: Articles
• Status: Unpublished
• Refereed: No
• Glasgow Author(s) Enlighten ID: Baker, Dr Andrew
• Authors: Baker, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: arXiv
• Copyright Holders: Copyright © 2020 The Author
• Publisher Policy: Reproduced with the permission of the Author