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Markus Land: Chromatic localizations of algebraic K-theory

Tid: Fr 2019-12-13 kl 15.15 - 17.00

Plats: Kräftriket, house 5, room 31

Medverkande: Markus Land, Universität Regensburg

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In the first part of the talk, I will present joint work with Georg Tamme about the failure of excision in algebraic K-theory. The theorem I will present will allow to treat any localizing invariant in place of K-theory. We will then single out particularly nice such invariants, which we call truncating. I will explain why truncating invariants are much more accessible to computations than general localizing invariants.

Algebraic K-theory itself is not truncating, and in the second part of the talk, I will present joint work with Lennart Meier and Georg Tamme in which we prove that K-theory, after localizing at Morava K-theories, is truncating on particular classes of rings, allowing for calculations of the chromatically localized K-theory of such rings. One prominent example is a recent theorem of Bhatt—Clausen—Mathew, which shows that the K(1)-localized K-theory of \(\mathbb{Z}/p^n\) vanishes. I will put this result into the context of certain invariants being truncating, and present a general theorem in this direction for all chromatic heights.