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On the K-theory of pullbacks

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HHH - Homotopy harnessing higher structures

In this talk I will report on joint work with Georg Tamme about excision results in K-theory and related invariants.   We show that, associated to any pullback square of E_1 ring spectra, there is an associated pullback diagram of K-theory spectra in which one of the corners is the K-theory of a new E_1 ring canonically associated to the original pullback diagram.   I will explain the main ingredients for the proof and then concentrate on simple consequences of this theorem. These include Suslin’s results on excision (for Tor-unital ideals) and the fact that (what we call) truncating invariants satisfy excision, nil invariance and cdh descent. If time permits I will also discuss how to deduce that in certain cases (bi)relative K-groups are torsion groups of bounded exponent, improving results of Geisser—Hesselholt.

This talk is part of the Isaac Newton Institute Seminar Series series.

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