The p-completed cyclotomic trace in degree 2

We prove that for a quasiregular semiperfectoid $ℤ_{p}^{c y c l}$ -algebra $R$ (in the sense of Bhatt–Morrow–Scholze), the cyclotomic trace map from the $p$ -completed $K$ -theory spectrum $K (R; ℤ_{p})$ of $R$ to the topological cyclic homology $TC (R; ℤ_{p})$ of $R$ identifies on $π_{2}$ with a $q$ -deformation of the logarithm.

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Keywords

algebraic $K\mkern-2mu$-theory, prisms, cyclotomic trace

Mathematical Subject Classification 2010

Primary: 19D55, 19F99

Milestones

Received: 4 November 2019

Revised: 2 April 2020

Accepted: 20 April 2020

Published: 28 July 2020

Authors

Johannes Anschütz
Mathematisches Institut Universität Bonn Bonn Germany

Arthur-César Le Bras
Institut Galilée Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539 Villetaneuse France

Vol. 5, No. 3, 2020

Johannes Anschütz and Arthur-César Le Bras

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors