Topological Hochschild homology of truncated Brown-Peterson spectra I
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916371338625024 |
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| author | Angelini-Knoll, Gabriel Culver, Dominic Leon Höning, Eva |
| author_facet | Angelini-Knoll, Gabriel Culver, Dominic Leon Höning, Eva |
| contents | We compute topological Hochschild homology of sufficiently structured forms of truncated Brown--Peterson spectra with coefficients. In particular, we compute $\mathrm{THH}_*(B\langle n\rangle ;H\mathbb{Z}_{(p)})$ for all $n$ and $\mathrm{THH}_*(B\langle 2\rangle ;M)$ for $M\in \{ k(1),k(2)\}$ where $B\langle n\rangle$ is an $E_3$ form of $BP\langle n\rangle$ for certain primes $p$. For example, this gives a computation of $\mathrm{THH}(\mathrm{taf}^{D};M)$ for $M\in \{H\mathbb{Z}_{(3)},k(1),k(1))$ where $\mathrm{taf}^{D}$ is the $E_{\infty}$ form of $BP\langle 2\rangle$ constructed by Hill--Lawson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_06785 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Topological Hochschild homology of truncated Brown-Peterson spectra I Angelini-Knoll, Gabriel Culver, Dominic Leon Höning, Eva Algebraic Topology K-Theory and Homology 55P42, 55P43, 55Q51, 55Q10, 16E40, 19D55, 55N22, 55T99 We compute topological Hochschild homology of sufficiently structured forms of truncated Brown--Peterson spectra with coefficients. In particular, we compute $\mathrm{THH}_*(B\langle n\rangle ;H\mathbb{Z}_{(p)})$ for all $n$ and $\mathrm{THH}_*(B\langle 2\rangle ;M)$ for $M\in \{ k(1),k(2)\}$ where $B\langle n\rangle$ is an $E_3$ form of $BP\langle n\rangle$ for certain primes $p$. For example, this gives a computation of $\mathrm{THH}(\mathrm{taf}^{D};M)$ for $M\in \{H\mathbb{Z}_{(3)},k(1),k(1))$ where $\mathrm{taf}^{D}$ is the $E_{\infty}$ form of $BP\langle 2\rangle$ constructed by Hill--Lawson. |
| title | Topological Hochschild homology of truncated Brown-Peterson spectra I |
| topic | Algebraic Topology K-Theory and Homology 55P42, 55P43, 55Q51, 55Q10, 16E40, 19D55, 55N22, 55T99 |
| url | https://arxiv.org/abs/2106.06785 |