SoSe 23 Oberseminar: Selmer K-theory
Time and place: Tuesday 14:15-15:45 in M311 and online
Selmer K-theory is a localizing invariant of stable categories introduced by Clausen to give a K-theoretic construction of the Artin map from the idele class group of a number field to its abelianized Galois group. For schemes, Selmer K-theory is closely related to the étale sheafification of algebraic K-theory, and in general it can thus be viewed as a non-commutative extension of the latter.
In this seminar, we will review the definition of Selmer K-theory, which combines insights of Thomason on K(1)-local algebraic K-theory and of Geisser–Hesselholt on topological cyclic homology. We will then discuss applications to étale K-theory following the paper:
- D. Clausen, A. Mathew, Hyperdescent and étale K-theory
For the definitions of Selmer K-theory and of topological cyclic homology we will use:
- D. Clausen, A K-theoretic approach to Artin maps
- T. Nikolaus, P. Scholze, On topological cyclic homology
| Date | Speaker | Topic |
|---|---|---|
| 18.04 | Niklas Kipp | Introduction |
| 25.04 | Marc Hoyois | Cyclotomic spectra and topological Hochschild homology |
| 02.05 | Lucas Piessevaux | Finiteness properties of TC |
| 09.05 | Marco Volpe | The cyclotomic trace |
| 16.05 | Ritheesh Krishna Thiruppathi | KU- and K(1)-localization |
| 23.05 | Niklas Kipp | The Geisser–Levine and Geisser–Hesselholt theorems |
| 30.05 | — | — |
| 06.06 | Gabriel Angelini-Knoll | The K-theory of henselian pairs |
| 13.06 | Christoph Winges | Preliminaries on hypersheaves |
| 20.06 | Giacomo Bertizzolo | The Nisnevich topos |
| 27.06 | Niko Naumann | The étale topos |
| 04.07 | Liam Keenan | Étale descent for TC and KU-localized invariants |
| 11.07 | Sebastian Wolf | Selmer K-theory and étale K-theory |