**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):

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

**Files for the class:**

- Syllabus
- Student presentations
- Problem Set 1
- Problem Set 2
- Problem Set 3
- Problem Set 4
- Problem Set 5
- Problem Set 6
- Problem Set 7
- Problem Set 8
- Practice Problems for the Exam

**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.