Every spectrum is the K-theory of a stable \(\infty\)-category

We prove that any spectrum is equivalent to the nonconnective K-theory of a stable \(\infty\)-category. We use these results to construct a stable \(\infty\)-category \(\mathcal{C}\) with a bounded t-structure such that \(\operatorname{K}(\mathcal{C})\) is not equivalent to \(\operatorname{K}(\mathc...

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Bibliographic Details
Published inarXiv.org
Main Authors Ramzi, Maxime, Sosnilo, Vladimir, Winges, Christoph
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.01.2024
Subjects
Equivalence
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Summary:We prove that any spectrum is equivalent to the nonconnective K-theory of a stable \(\infty\)-category. We use these results to construct a stable \(\infty\)-category \(\mathcal{C}\) with a bounded t-structure such that \(\operatorname{K}(\mathcal{C})\) is not equivalent to \(\operatorname{K}(\mathcal{C}^\heartsuit)\), disproving a conjecture of Antieau, Gepner, and Heller.
ISSN:2331-8422