Algebraic stacks, Winter semester 2020/21, by Georg Oberdieck

Date: Wednesday 4-6, Friday 12-2.
-----Update: January 13 No Lecture!

Location: Hoersaalzentrum, Endenicher Allee 19C - Hoersaal 1 (Basis link, Google link)
The lecture will take place in a hybrid format, that is regular lectures will be held in the above location, but can be joined via Zoom.
Update: Due to university decree the lecture will take place only online for the foreseeable future.

Zoom Meeting ID: 946 0820 8284
Passcode: Euler number of a K3 surface

Email: If you want to receive emails about the class, please sign up at eCampus.

First day of class: Wednesday Oct 28, 2020

Overview:The course is an introduction to the theory of algebraic stacks. We will discuss applications to the construction of moduli spaces.

Prerequisites: Algebraic Geometry I and II (e.g. on the level of Hartshorne's book Chapter I and II plus some background on flat/etale morphisms). Some category theory (such as Vakil's Notes on Algebraic Geometry, Chapter 1).

Some references (preliminary):

  1. Martin Olsson, Algebraic Spaces and Stacks
  2. Vistoli, Notes on Grothendieck topologies, fibered categories and descent theory (available online).
  3. Preliminary version of a book Algebraic Stacks by Behrend, Conrad, Edidin, Fantechi, Fulton, Goettsche, Kresch
  4. Deligne, Mumford, The irreducibility of the space of curves of given genus
  5. Halpern-Leistner, Moduli theory. (Notes from a course on algebraic stacks)
  6. The Stacks Project
  7. Guide to the literature by Jarod Alper

Files for the class:

  1. Syllabus
  2. Student presentations
  3. Problem Set 1
  4. Problem Set 2
  5. Problem Set 3
  6. Problem Set 4
  7. Problem Set 5
  8. Problem Set 6
  9. Problem Set 7
  10. Problem Set 8
  11. Practice Problems for the Exam
Solutions to the exercises can be handed in every Wednesday either in class, by uploading them in eCampus, or by placing them addressed to Denis Nesterov in the mailbox of the mathematical institute. Graded solutions will be returned one week later.

Exam requirement: There will be an oral exam. You have to hand in solutions to at least half of all exercise problems to be admitted to the exam.
Exam dates: February 19 and March 26, 2021.