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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06510 |
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| _version_ | 1866929207624335360 |
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| author | Ramzi, Maxime Sosnilo, Vladimir Winges, Christoph |
| author_facet | Ramzi, Maxime Sosnilo, Vladimir Winges, Christoph |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Every spectrum is the K-theory of a stable $\infty$-category Ramzi, Maxime Sosnilo, Vladimir Winges, Christoph K-Theory and Homology 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. |
| title | Every spectrum is the K-theory of a stable $\infty$-category |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2401.06510 |