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:

For the definitions of Selmer K-theory and of topological cyclic homology we will use:

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
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