Chromatic localizations of algebraic K-theory.

Abstract: A classic result of Waldhausen says essentially that algebraic K-theory preserves rational equivalences between connective ring spectra. From the viewpoint of chromatic homotopy theory, rationalization is just the zeroth level of chromatic localizations. Based on work of Clausen–Mathew–Naumann–Noel we showed in joint work with Land, Mathew and Tamme that in general the $n$-th chromatic level of the algebraic $K$-theory of a ring spectrum depends only on the $n$-th and $(n – 1)$-st chromatic level of the ring spectrum. This has in particular implications for red shift questions in the spirit of Ausoni and Rognes.

Mathematics

Audience: researchers in the topic

Opening Workshop (IRP Higher Homotopy Structures 2021, CRM-Bellaterra)