Very Schwartz coidempotents and continuous spectrum
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912366298398720 |
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| author | Aoki, Ko |
| author_facet | Aoki, Ko |
| contents | We introduce the continuous version of the (unstable) smashing spectrum functor. In the stable case, it assigns to each dualizably symmetric monoidal stable presentable $\infty$-category a stably compact space whose open subsets correspond to very Schwartz idempotents -- a certain class of idempotents we define. As an application, we prove Tannaka duality for spectral sheaves on stably compact spaces, including the case of compact Hausdorff spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Very Schwartz coidempotents and continuous spectrum Aoki, Ko Category Theory Algebraic Geometry Algebraic Topology General Topology We introduce the continuous version of the (unstable) smashing spectrum functor. In the stable case, it assigns to each dualizably symmetric monoidal stable presentable $\infty$-category a stably compact space whose open subsets correspond to very Schwartz idempotents -- a certain class of idempotents we define. As an application, we prove Tannaka duality for spectral sheaves on stably compact spaces, including the case of compact Hausdorff spaces. |
| title | Very Schwartz coidempotents and continuous spectrum |
| topic | Category Theory Algebraic Geometry Algebraic Topology General Topology |
| url | https://arxiv.org/abs/2505.04817 |