Introduction to algebraic K-theory

This is the website for the course I'm co-teaching with Kaif Hilman on algebraic K-theory in the summer semester of 2024 at the Max Planck Institute for Mathematics in Bonn.

Course: Introduction to algebraic K-theory

When: Wednesday 14.15 - 16.00 and Friday 10.15 - 12.00.

Where: MPIM Seminar Room

Lecture notes: Link 

The overall goal of this course is to cover the fundamental theorems of algebraic K-theory in the modern formalism of ∞-categories. We provisionally aim to cover the following topics:

• Preliminaries on ∞-categories

• Group completion K-theory and the group completion theorem

• Quillen's +-construction

• Algebraic K-theory of stable ∞-categories

• Waldhausen's additivity theorem

• The localization theorem

• The theorems of the heart

• K-theory of pullbacks after Land--Tamme

• Application: Purity in telescopically localized algebraic K-theory

Schedule:

Week 1:

24/4: Adjunctions, (co)limits, Bousfield localisations, Yoneda lemma, Dwyer--Kan localisations, and straightening/unstraightening. 

26/4: Semiadditivity and stability.

Week 2:

1/5: Holiday (Labour day)

3/5:

Week 3:

8/5:

10/5:

Week 4:

15/5:

17/5:

Week 5:

No lectures due to Pfingstferien.

Week 6:

29/5:

31/5:

Week 7: 

5/6:

7/6:

Week 8:

12/6 (at 12.15-14.00 in MPIM Lecture hall):

14/6:

Week 9:

19/6:

21/6:

Week 10: 

26/6: No lecture due to MPIM evaluation.

28/6:

Week 11:

3/7: 

5/7:

Week 12:

10/7: 

12/7:

Week 13:

17/7: 

19/7: