Topological Hochschild homology of truncated Brown-Peterson spectra II
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arXiv
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| Format: | Preprint |
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2026
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| author | Angelini-Knoll, Gabriel Chaminadour, Maxime |
| author_facet | Angelini-Knoll, Gabriel Chaminadour, Maxime |
| contents | We compute topological Hochschild homology of $\mathbb{E}_3$-MU-algebra forms of the second truncated Brown-Peterson spectrum with Adams summand coefficients at $p=2$ and conditionally at arbitrary primes. We also provide a new computational tool, a variant of the Brun spectral sequence, for computing topological Hochschild homology of truncated Brown-Peterson spectra with certain coefficients. As a consequence, we show that $\mathbb{E}_3$-MU-algebra forms of truncated Brown-Peterson spectra are not Thom spectra $\mathrm{BP}\langle n\rangle$ at the prime $p=2$ for any $n\ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11440 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological Hochschild homology of truncated Brown-Peterson spectra II Angelini-Knoll, Gabriel Chaminadour, Maxime Algebraic Topology K-Theory and Homology 55P42, 55P43, 55Q51, 55Q10, 16E40, 19D55, 55N22, 55T99 We compute topological Hochschild homology of $\mathbb{E}_3$-MU-algebra forms of the second truncated Brown-Peterson spectrum with Adams summand coefficients at $p=2$ and conditionally at arbitrary primes. We also provide a new computational tool, a variant of the Brun spectral sequence, for computing topological Hochschild homology of truncated Brown-Peterson spectra with certain coefficients. As a consequence, we show that $\mathbb{E}_3$-MU-algebra forms of truncated Brown-Peterson spectra are not Thom spectra $\mathrm{BP}\langle n\rangle$ at the prime $p=2$ for any $n\ge 2$. |
| title | Topological Hochschild homology of truncated Brown-Peterson spectra II |
| topic | Algebraic Topology K-Theory and Homology 55P42, 55P43, 55Q51, 55Q10, 16E40, 19D55, 55N22, 55T99 |
| url | https://arxiv.org/abs/2603.11440 |