SoSe 26 Oberseminar: Motivic cohomology of schemes
Time and place: Tuesday 14-16 in M311 and online
The goal of this seminar is to understand the motivic filtration of the A¹-invariant algebraic K-theory of arbitrary schemes and the resulting theory of A¹-invariant motivic cohomology, recently developed in this generality by Bachmann, Elmanto, and Morrow. The construction uses many aspects of the formalism of motivic spectra, including the slice filtration, the six-functor formalism, and framed correspondences, which we will review. We will then discuss the comparison with cycle-theoretic constructions in special cases (for smooth schemes over Dedekind rings) and with syntomic cohomology (the Beilinson–Lichtenbaum conjecture), and compute motivic cohomology in low weights.
The main reference is:
- Tom Bachmann, Elden Elmanto, Mathew Morrow, A¹-invariant motivic cohomology of schemes
If you are interested in participating in this seminar, please contact Marc Hoyois or Marco Volpe.
| Date | Speaker | Topic |
|---|---|---|
| 14.04 | Marc Hoyois | Motivic spectra, six functors, and cdh descent |
| 21.04 | Zhenming Xu | The slice filtration, the main theorem, and Voevodsky’s slice conjectures |
| 28.04 | Marc Hoyois | Framed correspondences |
| 05.05 | Marc Hoyois | The zeroth slice of the motivic sphere |
| 12.05 | Marco Volpe | Rational splitting |
| 19.05 | Ou Liu | Low weights |
| 26.05 | — | — |
| 02.06 | Han-Ung Kufner | Syntomic cohomology |
| 09.06 | Marc Hoyois | Beilinson–Lichtenbaum cohomology |
| 16.06 | Bastiaan Cnossen | Axiomatic Beilinson–Lichtenbaum isomorphism |
| 23.06 | Andrea Taccani | Beilinson–Lichtenbaum over Dedekind domains |
| 30.06 | Marco Volpe | Cdh-motivic cohomology |
| 07.07 | Niklas Kipp | A¹-invariance and projective bundle formula |
| 14.07 | Marco Volpe | Kato motivic cohomology and proof of the main theorem |