Stacks -- Fall 2022

Emory University

Notes
Syllabus
Homework
Resources
Lecture Room: E408 MSC
Lecture Time: TuTh 11:30-12:45
Final Exam: None
Lecturer:David Zureick-Brown
Office: W430 MSC
Phone: (608) 616-0153
Email: david.zureick.brown@gmail.com

Text: See below
Office Hours: TBD, (in W430)
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Syllabus

Algebraic stacks arise naturally as solutions to classification (moduli) problems, so it is desirable to understand their geometry. In this course, we will assume a working knowledge of the geometry of schemes. We will extend the definitions and techniques used to study schemes to algebraic spaces and algebraic stacks. We will give lots of motivation, examples, and applications. Topics will include Grothendieck topologies, descent, algebraic spaces, fibered categories, algebraic stacks, quotient stacks, deformation theory, torsors and gerbes. Additional topics will be included based on feedback from students.

Grading

There will be no exams or final. There will be regular homework. Students taking the course for a grade will receive homework instructions on Canvas.

Recordings: Recordings of the lectures are available here. (They will usually be posted within 24 hours.)

Notes: A PDF of notes is available here. (During the semester this will be more of a terse list of topics covered than a full set of notes, but eventually it will become more.) Office Hours: Office hours will (usually) be 2:30-3:30 on Mondays, via Zoom. The Zoom link will be available on Zulip. The first office hours will be Monday September 12.

Course dates: The course will meet Tuesdays and Thursdays 11:30-12:45. The first meeting will be on Thursday, August 25, and the final official meeting will be Tuesday, December 6. There will be no meetings on: August 30, September 1, October 11, and November 24.

Online participation: I will stream the course on Zoom, and there will be an associated Zulip chat associated with the course (open to everyone). The meetings will be recorded and posted to youtube.

If you would like to attend the online course, please send me an email at david.zureick.brown@gmail.com to let me know. You'll be added to a mailing list, and I will email you the zoom link the week of the course.

Book: The main textbook for the course will be Martin Olsson's "Algebraic Spaces and Stacks".

Other Resources
Background Resources

Highly recommended reading -- to get a sense of the various perspectives on and roles played by stacks (and algebraic spaces), please take a look at each of the following.