Vol. 5, No. 3, 2020

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

Johannes Anschütz and Arthur-César Le Bras

Vol. 5 (2020), No. 3, 539–580
Abstract

We prove that for a quasiregular semiperfectoid pcycl-algebra R (in the sense of Bhatt–Morrow–Scholze), the cyclotomic trace map from the p-completed K-theory spectrum K(R; p) of R to the topological cyclic homology TC(R; p) of R identifies on π2 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