Chromatic Cardinalities via Redshift
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911897674055680 |
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| author | Ben-Moshe, Shay Carmeli, Shachar Schlank, Tomer M. Yanovski, Lior |
| author_facet | Ben-Moshe, Shay Carmeli, Shachar Schlank, Tomer M. Yanovski, Lior |
| contents | Using higher descent for chromatically localized algebraic $K$-theory, we show that the higher semiadditive cardinality of a $π$-finite $p$-space $A$ at the Lubin-Tate spectrum $E_n$ is equal to the higher semiadditive cardinality of the free loop space $LA$ at $E_{n-1}$. By induction, it is thus equal to the homotopy cardinality of the $n$-fold free loop space $L^n A$. We explain how this allows one to bypass the Ravenel-Wilson computation in the proof of the $\infty$-semiadditivity of the $T(n)$-local categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00275 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Chromatic Cardinalities via Redshift Ben-Moshe, Shay Carmeli, Shachar Schlank, Tomer M. Yanovski, Lior Algebraic Topology K-Theory and Homology Using higher descent for chromatically localized algebraic $K$-theory, we show that the higher semiadditive cardinality of a $π$-finite $p$-space $A$ at the Lubin-Tate spectrum $E_n$ is equal to the higher semiadditive cardinality of the free loop space $LA$ at $E_{n-1}$. By induction, it is thus equal to the homotopy cardinality of the $n$-fold free loop space $L^n A$. We explain how this allows one to bypass the Ravenel-Wilson computation in the proof of the $\infty$-semiadditivity of the $T(n)$-local categories. |
| title | Chromatic Cardinalities via Redshift |
| topic | Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2310.00275 |