SoSe 25 Oberseminar: The Bloch–Kato conjecture
Time and place: Tuesday 14:15-15:45 in M311 and online
The goal of this seminar is to discuss two aspects of Voevodsky’s chromatic approach to the Bloch–Kato conjecture, which together with last semester’s seminar complete the proof of the conjecture. Specifically, we will:
- Prove the Hopkins–Morel isomorphism relating algebraic cobordism and motivic cohomology.
- Construct Rost motives, which are higher chromatic analogues of motives of finite field extensions.
The main ingredient for both results is the determination of the motivic Steenrod algebra, which is the algebra of bistable operations in motivic cohomology with coefficients in Z/l.
| Date | Speaker | Topic |
|---|---|---|
| 29.04 | Marc Hoyois | Power operations in motivic cohomology |
| 06.05 | Bastiaan Cnossen | The motivic Steenrod algebra |
| 13.05 | Pavel Sechin | The Milnor operations |
| 20.05 | Runlei Xiao | Symmetric powers of Tate motives |
| 27.05 | Vova Sosnilo | Motives of Eilenberg–Mac Lane spaces |
| 03.06 | Sebastian Wolf | The motivic cohomology of quotients of MGL |
| 10.06 | — | — |
| 17.06 | Tess Bouis | The Hopkins–Morel isomorphism |
| 24.06 | The motivic degree theorem | |
| 01.07 | A uniqueness theorem for motivic Steenrod operations | |
| 08.07 | Cohomology operations from symmetric powers | |
| 15.07 | Generalized Rost motives | |
| 22.07 | The Bloch–Kato conjecture |