Stacks -- Fall 2012

Emory University

Lecture Room: E408 MSC
Lecture Time: TuTh 1:00-2:15
Final Exam: None
Lecturer:David Zureick-Brown
Office: W430 MSC
Phone: (608) 616-0153

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



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.


There will be no exams or final. There will be lots of homework. N.B. Instead, there will be an additional extra weekly meeting/office hours (to be set once the semester begins) in which we will discuss the homework problems and review background material.


Pdf of notes.

The notes for this course are a modified copy of the notes that Anton Geraschenko live-TeXed from Martin Olsson's Spring 2007 course on stacks at UC Berkeley. We will not follow these notes exactly; I class I am planning longer digressions on background material, and will omit many of the topics of Martin's notes.
Please, whenever possible, do me (and classmates, rest of the world, etc) a favor and send me a short email whenever you find an error in the notes [and there are errors!]. (Better -- if you replace `Stacks.pdf' in the url with, e.g., `StackLec12.tex', this will produce the source file for that lecture. )


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. (More to come.)