Lectures on presheaves of spectra
The pdf files below are my lecture notes from a course on presheaves
of spectra, which I gave at the University of Western Ontario
during the Fall term of 2005.
The background for this course includes my previous course on
simplicial presheaves, the lecture notes for which can be found at my
The notes are rough so far, but will improve with the progress of time
- the indicated dates are last updates. There are some hypertext
links in the files, and suggestions on how to improve their utility
would be welcome.
Comments or suggestions about these files are welcome, at email@example.com.
- Lecture 001: Basic facts: simplicial sets, pointed simplicial sets, spectra
- Lecture 002: Spectra, the stable category
- Lecture 003: Basic stable homotopy theory: suspensions and shifts, additivity, fibre and cofibre sequences
- Lecture 004: Derived categories: simplicial modules, spectrum objects in simplicial modules, chain complexes
- Lecture 005: Some Grothendieck sites, simplicial presheaves, presheaves of spectra
- Lecture 006: T-spectra, localization
- Lecture 007: Stably fibrant models, injective and stable fibrations, bispectra and bigraded stable homotopy groups
- Lecture 008: T-spectrum theories, Brown-Gersten and Nisnevich descent theorems
- Lecture 009: f-local stable categories, motivic stable categories, motivic stable homotopy groups
- Lecture 010: Symmetric spaces, symmetric T-spectra, injective model structure, localized model structures
- Lecture 011: Stable homotopy theory of symmetric T-spectra, the smash product