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:

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
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