Algebraicity in monochromatic homotopy theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908729098633216 |
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| author | Aambø, Torgeir |
| author_facet | Aambø, Torgeir |
| contents | Using Patchkoria--Pstrągowski's version of Franke's algebraicity theorem, we prove that the category of $K_p(n)$-local spectra is exotically equivalent to the category of derived $I_n$-complete periodic comodules over the Adams Hopf algebroid $(E_*, E_*E)$ for large primes. This gives a finite prime result analogous to the asymptotic algebraicity for $\mathrm{Sp}_{K_p(n)}$ of Barthel--Schlank--Stapleton. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraicity in monochromatic homotopy theory Aambø, Torgeir Algebraic Topology Using Patchkoria--Pstrągowski's version of Franke's algebraicity theorem, we prove that the category of $K_p(n)$-local spectra is exotically equivalent to the category of derived $I_n$-complete periodic comodules over the Adams Hopf algebroid $(E_*, E_*E)$ for large primes. This gives a finite prime result analogous to the asymptotic algebraicity for $\mathrm{Sp}_{K_p(n)}$ of Barthel--Schlank--Stapleton. |
| title | Algebraicity in monochromatic homotopy theory |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2403.07725 |