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arXiv · 2410.07048

Syntomic cohomology of Morava K-theory

Gabriel Angelini-Knoll·Jeremy Hahn·Dylan Wilson
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Abstract

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 $\pi_*TC(k(n))_p$ is concentrated on at most three lines, independently of $n$.

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Gabriel Angelini-Knoll, Jeremy Hahn, Dylan Wilson. 2024-10-09. Syntomic cohomology of Morava K-theory. https://arxiv.org/abs/2410.07048

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