Math 615A

Introducion to Algebraic Stacks

Fall  2019      Course Information

Time: MWF 10:00-10:50

Place: Math Annex 1118.

Instructor: Kai Behrend

Office hours:

Wed 3-4, Thu 2-3
in Math 227.

Prerequisites: One semester of algebraic geometry, such as Math 532. Some familiarity with varieties, in particular the geometry of curves.

Course Outline: This will be an introduction to algebraic stacks.

The first part (maybe 3-4 weeks) will be a very gentle introduction to the ideas of stacks in general. The only prerequisites for this part are some undergraduate topology, and some undergraduate group theory.

The second part (maybe 3-4 weeks) will cover some basic theory of algebraic stacks, leading to the Riemann-Roch theorem for Deligne-Mumford curves.

For the first two parts, we will follow the notes which constitute the first chapter of this volume on Moduli Spaces. (You should have access through the UBC library.)

Here is a file .

The material we discuss in the rest of the course will largely depend on audience interest. One possibility is to cover higher stacks.

Marking: Your mark will be based on a project. Your project will be determined jointly by you and the instructor.