Lectures on Local Homotopy Theory

The pdf files below are my lecture notes for a course on local homotopy theory (aka. homotopy theory of simplicial presheaves and presheaves of spectra) which was given at the University of Western Ontario in 2009 and 2010.

All files are still subject to change - the indicated dates are last updates.

If you have comments or suggestions about these files, please do not hesitate to contact me: jardine@uwo.ca.

• Lecture 01: Simplicial sets, Simplicial homotopy theory (01/07/09)

• Lecture 02: Grothendieck toposes, geometric morphisms, Boolean localization (01/18/09)

• Lecture 03: Rigidity (09/23/10)

• Lecture 04: Local weak equivalences, local fibrations (11/01/10)

• Lecture 05: Model structures: simplicial presheaves and simplicial sheaves (10/22/10)

• Lecture 06: Simplicial modules, derived category (11/01/10)

• Lecture 07: Cocycles, sheaf cohomology, descent spectral sequences (01/06/11)

• Lecture 08: Torsors for groups and groupoids, stacks and homotopy theory (01/06/11)

• Lecture 09: The Verdier hypercovering theorem (02/27/09)

• Lecture 10: Localization for simplicial presheaves (01/06/11)

• Lecture 11: Presheaves of spectra, the stable category (01/06/11)

• Lecture 12: T-spectra (03/27/09)

• Lecture 13: Brown-Gersten and Nisnevich descent, motivic descent (03/30/09)

• Lecture 14: Stable homotopy theory of T-spectra (04/06/09)

• References (03/30/09)