Syntomic cohomology of Morava K-theory
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909574602162176 |
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| author | Angelini-Knoll, Gabriel Hahn, Jeremy Wilson, Dylan |
| author_facet | Angelini-Knoll, Gabriel Hahn, Jeremy Wilson, Dylan |
| contents | We compute the MU-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n+1})$, of all $\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope conjecture, and redshift conjecture for the algebraic K-theories of all $\mathbb{E}_{1}$-$\mathbb{S}$-algebra forms of $(2p^n-2)$-periodic Morava K-theory. Notably, the motivic spectral sequence computing $π_*TC(k(n))_p$ is concentrated on at most three lines, independently of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Syntomic cohomology of Morava K-theory Angelini-Knoll, Gabriel Hahn, Jeremy Wilson, Dylan K-Theory and Homology Algebraic Topology 19D55, 55Q51, 55P43, 14F30, 19D50 (Primary) 13D03, 19E20, 55N15, 55T15, 55T25 (Secondary) We compute the MU-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n+1})$, of all $\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope conjecture, and redshift conjecture for the algebraic K-theories of all $\mathbb{E}_{1}$-$\mathbb{S}$-algebra forms of $(2p^n-2)$-periodic Morava K-theory. Notably, the motivic spectral sequence computing $π_*TC(k(n))_p$ is concentrated on at most three lines, independently of $n$. |
| title | Syntomic cohomology of Morava K-theory |
| topic | K-Theory and Homology Algebraic Topology 19D55, 55Q51, 55P43, 14F30, 19D50 (Primary) 13D03, 19E20, 55N15, 55T15, 55T25 (Secondary) |
| url | https://arxiv.org/abs/2410.07048 |