SoSe 21 Oberseminar: Hermitian K-theory of rings
Time and place: Tuesday 14:15-15:45 online
The goal of this seminar is to study some recent developments on the Hermitian K-theory of rings of integers following Calmès, Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus, and Steimle. A particular focus will be on the complete solution of Thomason’s homotopy limit problem for number rings, which states that the Grothendieck–Witt spectrum of a number ring is 2-adically equivalent to the homotopy C₂-fixed points of its K-theory spectrum. In particular we will review the solution of this problem for fields using motivic homotopy techniques, following Bachmann and Hopkins.
The main references are:
- Hermitian K-theory for stable ∞-categories III: Grothendieck–Witt groups of rings
- η-periodic motivic stable homotopy theory over fields (Appendix A and references therein)
| Date | Speaker | Topic |
|---|---|---|
| 27.04 | Marc Hoyois | Introduction |
| 04.05 | Niklas Kipp | The homotopy t-structure on motivic spectra |
| 11.05 | Pavel Sechin | The motivic Hermitian K-theory spectrum |
| 18.05 | Denis Nardin | Voevodsky’s slice filtration and Levine’s coniveau filtration |
| 25.05 | Tom Bachmann | The convergence of the slice filtration |
| 01.06 | — | — |
| 08.06 | Marc Hoyois | The slices of Hermitian K-theory and the homotopy limit problem away from 2 |
| 15.06 | Luca Pol | Algebraic surgery |
| 22.06 | Lucy Yang | Regular coherent rings |
| 29.06 | Elden Elmanto | Dévissage in Hermitian K-theory and the localization sequence |
| 06.07 | Denis Nardin | The homotopy limit problem for rings of integers |