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The $p$-completed cyclotomic trace in degree $2$ (1907.10530v2)
Published 24 Jul 2019 in math.KT and math.NT
Abstract: We prove that for a quasi-regular semiperfectoid $\mathbb{Z}_p{\rm cycl}$-algebra $R$ (in the sense of Bhatt-Morrow-Scholze), the cyclotomic trace map from the $p$-completed $K$-theory spectrum $K(R;\mathbb{Z}_p)$ of $R$ to the topological cyclic homology $\mathrm{TC}(R;\mathbb{Z}_p)$ of $R$ identifies on $\pi_2$ with a $q$-deformation of the logarithm.
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