Descent spectral sequences through synthetic spectra
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866918078536744960 |
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| author | Carrick, Christian Davies, Jack Morgan van Nigtevecht, Sven |
| author_facet | Carrick, Christian Davies, Jack Morgan van Nigtevecht, Sven |
| contents | The synthetic analogue functor $ν$ from spectra to synthetic spectra does not preserve all limits. In this paper, we give a necessary and sufficient criterion for $ν$ to preserve the global sections of a derived stack. Even when these conditions are not satisfied, our framework still yields synthetic spectra that implement the descent spectral sequence for the structure sheaf, thus placing descent spectral sequences on good footing in the $\infty$-category of synthetic spectra. As an example, we introduce a new $\mathrm{MU}$-synthetic spectrum $\mathrm{Smf}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01507 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Descent spectral sequences through synthetic spectra Carrick, Christian Davies, Jack Morgan van Nigtevecht, Sven Algebraic Topology The synthetic analogue functor $ν$ from spectra to synthetic spectra does not preserve all limits. In this paper, we give a necessary and sufficient criterion for $ν$ to preserve the global sections of a derived stack. Even when these conditions are not satisfied, our framework still yields synthetic spectra that implement the descent spectral sequence for the structure sheaf, thus placing descent spectral sequences on good footing in the $\infty$-category of synthetic spectra. As an example, we introduce a new $\mathrm{MU}$-synthetic spectrum $\mathrm{Smf}$. |
| title | Descent spectral sequences through synthetic spectra |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2407.01507 |