## GRK 2240 Lecture (winter term 19/20): From Chow groups to motivic homotopy theory

### Thursday, 14:00-15:30, room F.13.11

### table of contents (preliminary):

0. Algebraic topology: recollections, survey and motivation

1. Chow groups

2. Pure motives

3. Motivic cohomology and mixed motives

4. Milnor- and Bloch-Kato conjecture

5. Algebraic K-theory

6.H(k) and SH(k): Constructions, elementary properties and computations

7. Other generalized motivic cohomology theories

8. Rigidity

9. The motivic Atiyah-Hirzebruch spectral sequence

10. Algebraic cobordism and applications

11. Chow-Witt groups and algebraic vector bundles

Intitially, I planned to have a chapter "Applications to enumerative geometry"
after the chapter on "Chow groups". This chapter has been cancelled because of
this seminar in Düsseldorf which I strongly recommend, and which will assume some results I establish in chapter 1 of my lecture.
Also, as the title indicates, chapters 1 and 6 will be longer than the others.
Section 5 will be rather short, as I already lectured on K-theory during the Ringvorlesung in July 2019.

References (will be extended as the term continues)

I offer an additional lecture on Monday, 14:15 to 15:45, in lecture hall 3,
for Master students in Wuppertal. This lecture will be on related topics
in topology, for instance topological cobordism. Sometimes I will also explain
elementary material from algebraic geometry which might help Master students to understand the lecture on Thursday. Both lectures combined are "Spezielle Kapitel" and Master students enrolled in Wuppertal may take an exam on this at the end of the term.