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Talk

November 17th 2020
Georg Tamme (Universität Regensburg): Purity in chromatically localized algebraic K-theory

Abstract

A classical result of Waldhausen implies that a map of connective ring spectra which is a \pi_0-isomorphism and a rational equivalence induces an equivalence on rational algebraic K-theory. In this talk I will discuss a higher chromatic analog of this statement: Any map of ring spectra which is a T(n-1)+T(n) equivalence induces an equivalence on T(n)-local K-theory. This easily implies several vanishing results for chromatic localizations of the K-theory of ring spectra.

This is based on joint work with Markus Land, Akhil Mathew, and Lennart Meier and on closely related work of Dustin Clausen, Akhil Mathew, Niko Naumann, and Justin Noel.

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