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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Accesso online: | https://arxiv.org/abs/2110.03733 |
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| _version_ | 1866915716170514432 |
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| author | Blumberg, Andrew J. Mandell, Michael A. Yuan, Allen |
| author_facet | Blumberg, Andrew J. Mandell, Michael A. Yuan, Allen |
| contents | We show that the map from $K({\mathbb S})$ to its chromatic completion is a connective cover and identify the fiber in $K$-theoretic terms. We combine this with recent work of Land-Mathew-Meier-Tamme to prove a form of "Waldhausen's Chromatic Convergence Conjecture": we show that the map $K({\mathbb S}_{(p)})_{(p)}\to \mathop{\rm holim} K(L^{f}_{n}{\mathbb S})_{(p)}$ is the inclusion of a wedge summand. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_03733 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Chromatic convergence for the algebraic K-theory of the sphere spectrum Blumberg, Andrew J. Mandell, Michael A. Yuan, Allen K-Theory and Homology Algebraic Topology Primary 19D10, Secondary 55P60 We show that the map from $K({\mathbb S})$ to its chromatic completion is a connective cover and identify the fiber in $K$-theoretic terms. We combine this with recent work of Land-Mathew-Meier-Tamme to prove a form of "Waldhausen's Chromatic Convergence Conjecture": we show that the map $K({\mathbb S}_{(p)})_{(p)}\to \mathop{\rm holim} K(L^{f}_{n}{\mathbb S})_{(p)}$ is the inclusion of a wedge summand. |
| title | Chromatic convergence for the algebraic K-theory of the sphere spectrum |
| topic | K-Theory and Homology Algebraic Topology Primary 19D10, Secondary 55P60 |
| url | https://arxiv.org/abs/2110.03733 |