Syntomic cohomology of Morava K-theory

2024/10/09 by Angelini-Knoll, Gabriel, Hahn, Jeremy, Wilson, Dylan
#14F30 #19D50 (Primary) 13D03 #19D55 #19E20 #55N15 #55P43 #55Q51 #55T15 #55T25 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2410.07048

Abstract

We compute the MU-based syntomic cohomologies, mod (p,v₁,⋯,v_n+1), of all 𝔼₁-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 𝔼₁-\mathbbS-algebra forms of (2pⁿ-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.

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