Syntomic cohomology of truncated Brown--Peterson spectra
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914339078799360 |
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| author | Angelini-Knoll, Gabriel |
| author_facet | Angelini-Knoll, Gabriel |
| contents | We compute the $\mathrm{MU}$-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n})$, of all $\mathbb{E}_1$ $\mathrm{MU}$-algebra forms of the truncated Brown--Peterson spectrum $\mathrm{BP}\langle n\rangle$. As qualitative consequences, we resolve the Lichtenbaum--Quillen, telescope, and redshift questions for the algebraic K-theories of all $\mathbb{E}_{1}$ $\mathrm{MU}$-algebra forms of $\mathrm{BP} \langle n\rangle$. This extends work of the Hahn and Wilson. We also explicitly compute the algebraic K-theory of arbitrary $\mathbb{E}_{1}$ $\mathrm{MU}$-algebra forms of $\mathrm{BP}\langle 2\rangle$ at all primes $p\ge 5$ extending previous work of the author, Ausoni, Culver, Höning, and Rognes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14380 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Syntomic cohomology of truncated Brown--Peterson spectra Angelini-Knoll, Gabriel K-Theory and Homology Algebraic Topology 19D55, 55Q51, 55P43, 14F30, 19D50 (Primary) 13D03, 19E20, 55T15, 55T25, 19E15 (Secondary) We compute the $\mathrm{MU}$-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n})$, of all $\mathbb{E}_1$ $\mathrm{MU}$-algebra forms of the truncated Brown--Peterson spectrum $\mathrm{BP}\langle n\rangle$. As qualitative consequences, we resolve the Lichtenbaum--Quillen, telescope, and redshift questions for the algebraic K-theories of all $\mathbb{E}_{1}$ $\mathrm{MU}$-algebra forms of $\mathrm{BP} \langle n\rangle$. This extends work of the Hahn and Wilson. We also explicitly compute the algebraic K-theory of arbitrary $\mathbb{E}_{1}$ $\mathrm{MU}$-algebra forms of $\mathrm{BP}\langle 2\rangle$ at all primes $p\ge 5$ extending previous work of the author, Ausoni, Culver, Höning, and Rognes. |
| title | Syntomic cohomology of truncated Brown--Peterson spectra |
| topic | K-Theory and Homology Algebraic Topology 19D55, 55Q51, 55P43, 14F30, 19D50 (Primary) 13D03, 19E20, 55T15, 55T25, 19E15 (Secondary) |
| url | https://arxiv.org/abs/2602.14380 |