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

Maxime Ramzi; Vladimir Sosnilo; Christoph Winges

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arXiv · 2401.06510

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

Maxime Ramzi·Vladimir Sosnilo·Christoph Winges

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Abstract

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.

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BibTeX RIS

Maxime Ramzi, Vladimir Sosnilo, Christoph Winges. 2024-01-12. Every spectrum is the K-theory of a stable $\infty$-category. https://arxiv.org/abs/2401.06510

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