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Ben Antieau (Illinois): Negative and homotopy K-theory of ring spectra and extensions of the theorem of the heart (10/05/2016)


Barwick proved that the K-theory of a stable infinity-category with a bounded $t$-structure agrees with the K-theory of its heart in non-negative degrees. Joint work with David Gepner and Jeremiah Heller extends this to an equivalence of nonconnective K-theory spectra when the heart satisfies certain finiteness conditions such as noetherianity. Applications to negative K-theory and homotopy K-theory of ring spectra are provided, which were the original motivation for our work.

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