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Syntomic cohomology of Morava K-theory

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arxiv 2410.07048 v2 pith:ADTAJ6LF submitted 2024-10-09 math.KT math.AT

Gabriel Angelini-Knoll , Jeremy Hahn , Dylan Wilson This is my paper · ORCID
classification math.KTmath.AT
keywords conjecturek-theorymathbbmoravaformssyntomicalgebraalgebraic
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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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  1. On the integral algebraic K-theory of Morava K-theory

    math.AT 2026-07 conditional novelty 8.0 of 10

    For connective Morava K-theory, the paper determines algebraic K-theory group cardinalities in all degrees outside two congruence classes over finite fields, and proves even-degree groups vanish over algebraically clo...

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