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arXiv · 1907.10530

The $p$-completed cyclotomic trace in degree $2$

Johannes Anschütz·Arthur-César Le Bras
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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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BibTeXRIS

Johannes Anschütz, Arthur-César Le Bras. 2019-07-24. The $p$-completed cyclotomic trace in degree $2$. https://doi.org/10.2140/akt.2020.5.539

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