nLab Rings, modules and algebras in stable homotopy theory

This page collects material related to

• Anthony Elmendorf, Igor Kriz, Michael Mandell, Peter May,

  Rings, modules and algebras in stable homotopy theory

  Mathematical Surveys and Monographs Volume 47

  AMS 1997

  ISBN:978-0-8218-4303-1

  pdf

on higher algebra (brave new algebra) in stable homotopy theory, i.e. on ring spectra, module spectra etc.

(Sometimes referred to as EKMM for short, after the initials of its authors.)

This was the first account to give a symmetric monoidal category of spectra (here modered as “S-modules”), in which $A_\infty$ and $E_\infty$-ring spectra could be defined as ordinary monoids and their modules.

Chapter I. Prologue: the category of $\mathbb{L}$-spectra

• coordinate-free spectrum

Chapter II. Structured ring and module spectra

• ring spectrum

• module spectrum

Chapter III. The homotopy theory of $R$-Modules

Chapter IV. The algebraic theory of $R$-modules

Chapter V. $R$-Ring spectra and the specialization to $MU$

• MU

Chapter VI. Algebraic K-theory of $S$-algebras

• algebraic K-theory

Chapter VII. $R$-algebras and topological model categories

Chapter VIII. Bousfield localization of $R$-modules and algebras

Chapter IX. Topological Hochschild homology and cohomology

• topological Hochschild homology

Chapter X. Some basic constructions on spectra

Chapter XI. Spaces of linear isometries and technical theorems

Chapter XII. The monadic bar construction

Chapter XIII. Epilogue. The category of $\mathbb{L}$-spectra under $S$

category: reference