The pdf files below are my lecture notes for a course on local homotopy theory, or the homotopy theory of simplicial sheaves presheaves and presheaves of spectra.

In addition to these notes, the basic source material for the course is the book **Local Homotopy Theory**, by J.F. Jardine (Springer-Verlag, 2015). Supplemental reading is given in the list of References.

The syllabus for the course is the list of file names below. All files are subject to revision as the course progresses. The indicated dates are the most recent file updates. This web page is the primary source of information for the course.

The course is given as a set of lectures at the University of Western Ontario, and is available by teleconference to students from other universities. Students from other sites can participate, from either traditional teleconference rooms or by using suitably equipped personal computers. Please contact me if you wish to do so.

The grades for students registered in the course at Western will be based on lectures that they present in class. For students at another site, it is convenient that a local instructor set up a reading course, which would be graded by using a method of his or her choice.

The course meets on **Monday, Wednesday and Friday 13:00-14:00, Toronto time**. The first lecture was on September 12.

If you have any comments or questions about the course, please do not hesitate to contact me:

J.F. Jardine

Department of Mathematics

Office: MC 118

Phone: 1-519-661-2111 x86512

E-mail: jardine@uwo.ca.

**Accommodations for illness**

Such accommodations can be made, almost always by an informal procedure.

For the undergraduate University Policy on Accommodation for Illness and a downloadable SMC see: http://www.uwo.ca/univsec/pdf/academic_policies/appeals/accommodation_illness.pdf [downloadable Student Medical Certificate (SMC): http://www.uwo.ca/univsec/pdf/academic_policies/appeals/medicalform.pdf]

**Scholastic offences**

Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at the following Web site: http://www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_grad.pdf

**New:** **Recorded Lectures**

- Lecture 01:
**Simplicial sets, Simplicial homotopy theory**(09/14/16) - Lecture 02:
**Grothendieck toposes, geometric morphisms, Boolean localization**(09/19/16) - Lecture 03:
**Rigidity**(09/12/16) - Lecture 04:
**Local weak equivalences, local fibrations**(09/26/16) - Lecture 05:
**Model structures: simplicial presheaves and simplicial sheaves**(09/14/16) - Lecture 06:
**Simplicial modules, derived category**(10/06/16) - Lecture 07:
**Cocycles, sheaf cohomology, descent spectral sequences**(10/19/16) - Lecture 08:
**Torsors for groups and groupoids, stacks and homotopy theory**(10/26/16) - Lecture 09:
**The Verdier hypercovering theorem**(11/02/16) - Lecture 10:
**Localization for simplicial presheaves**(11/18/16) - Lecture 11:
**Presheaves of spectra, the stable category**(12/07/16) - Lecture 12:
**T-spectra**(12/07/16) - Lecture 13:
**Brown-Gersten and Nisnevich descent, motivic descent**(03/30/09) - Lecture 14:
**Stable homotopy theory of T-spectra**(04/06/09) - References (10/07/16)