Vol. 5, No. 3, 2020
Download this article
Download this article For screen
For printing
Recent Issues
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2379-1691 (online)
ISSN 2379-1683 (print)
 
Author index
To appear
 
Other MSP journals
The $p$-completed cyclotomic trace in degree $2$

Johannes Anschütz and Arthur-César Le Bras
Vol. 5 (2020), No. 3, 539–580
DOI: 10.2140/akt.2020.5.539
Abstract

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

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