The smashing spectrum of sheaves
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916277772091392 |
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| author | Aoki, Ko |
| author_facet | Aoki, Ko |
| contents | For an arbitrary $\infty$-topos, we classify the smashing localizations in the $\infty$-category of sheaves valued in derived vector spaces: Any of them is the restriction functor to a (unique) closed subtopos. Our proof is based on the existence of a Boolean cover.
This result in particular gives us the first example of a nonzero presentably symmetric monoidal stable $\infty$-category whose smashing spectrum has no points.
Combining this with the sheaves-spectrum adjunction, we obtain a Tannaka-type categorical reconstruction result for locales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The smashing spectrum of sheaves Aoki, Ko Category Theory Commutative Algebra Algebraic Topology For an arbitrary $\infty$-topos, we classify the smashing localizations in the $\infty$-category of sheaves valued in derived vector spaces: Any of them is the restriction functor to a (unique) closed subtopos. Our proof is based on the existence of a Boolean cover. This result in particular gives us the first example of a nonzero presentably symmetric monoidal stable $\infty$-category whose smashing spectrum has no points. Combining this with the sheaves-spectrum adjunction, we obtain a Tannaka-type categorical reconstruction result for locales. |
| title | The smashing spectrum of sheaves |
| topic | Category Theory Commutative Algebra Algebraic Topology |
| url | https://arxiv.org/abs/2406.03969 |