Integral topological Hochschild homology of connective complex K-theory
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912928625590272 |
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| author | Lee, David Jongwon |
| author_facet | Lee, David Jongwon |
| contents | We compute the homotopy groups of $\mathrm{THH}(\mathrm{ku})$ as a $\mathrm{ku}_\ast$-module using the descent spectral sequence for the map $\mathrm{THH}(\mathrm{ku})\to\mathrm{THH}(\mathrm{ku}/\mathrm{MU})$, which is the motivic spectral sequence for $\mathrm{THH}(\mathrm{ku})$ in the sense of Hahn-Raksit-Wilson. We reduce the computation of homotopy groups to the algebra of the universal formal group law, providing a systematic way to compute THH of quotients of MU. We compute the $E_2$-page of the motivic spectral sequence computing $\mathrm{THH}(\mathrm{ku})$, and we show that it degenerates at the $E_2$-page. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02411 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Integral topological Hochschild homology of connective complex K-theory Lee, David Jongwon Algebraic Topology K-Theory and Homology We compute the homotopy groups of $\mathrm{THH}(\mathrm{ku})$ as a $\mathrm{ku}_\ast$-module using the descent spectral sequence for the map $\mathrm{THH}(\mathrm{ku})\to\mathrm{THH}(\mathrm{ku}/\mathrm{MU})$, which is the motivic spectral sequence for $\mathrm{THH}(\mathrm{ku})$ in the sense of Hahn-Raksit-Wilson. We reduce the computation of homotopy groups to the algebra of the universal formal group law, providing a systematic way to compute THH of quotients of MU. We compute the $E_2$-page of the motivic spectral sequence computing $\mathrm{THH}(\mathrm{ku})$, and we show that it degenerates at the $E_2$-page. |
| title | Integral topological Hochschild homology of connective complex K-theory |
| topic | Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2206.02411 |