Introduction to derived algebraic geometry

Summer 2025, Regensburg

Contents

We introduce the basic concepts in derived algebraic geometry—such as animated rings, derived schemes, derived algebraic stacks, and quasi-coherent modules—and discuss their basic properties. This course aims to discuss an algebraicity result of Weil restrictions.

Exam

Please let my know (for example by e-mail) as soon as possible if you want to take an exam. These will be oral and by appointment.

When and where

Fridays from 10:15 till 11:45 in M101. The first meeting is 25th of April. 

You can also attend on Zoom via this link.  The passcode is 307612.

Planning & recordings

Here is the preliminary planning (subject to change), and links to recordings (with the same password as for the Zoom meetings):

There are some lectures for which there is no recording due to various technical difficulties.

Course notes

See here for the course notes. 

Warning: These course notes are extremely unfinished. Expect some results to be at least slightly wrong, and many arguments to change in the future. I intend to return to these notes in a few months as of now (Oct. 2025). When they reach a more stable version I will update the website to indicate this. 

Addendum

1. During Lecture 2 in the definition of a filtered category C I should have said that the poset A is supposed to be finite (corrected in the notes).

2. During Lecture 8 whenever I say `1-algebraic' it should be '0-algebraic' (corrected in the notes).