Mathematical Research Letters

Volume 25 (2018)

Number 2

On higher topological Hochschild homology of rings of integers

Pages: 489 – 507



Bjørn Ian Dundas (Department of Mathematics, University of Bergen, Norway)

Ayelet Lindenstrauss (Department of Mathematics, Indiana University, Bloomington In., U.S.A.)

Birgit Richter (Fachbereich Mathematik, Universität Hamburg, Germany)


We determine higher topological Hochschild homology of rings of integers in number fields with coefficients in suitable residue fields. We use the iterative description of higher $THH$ for this and Postnikov arguments that allow us reduce the necessary computations to calculations in homological algebra, starting from the results of Bökstedt and Lindenstrauss–Madsen on (ordinary) topological Hochschild homology.

This material is based upon work supported by the National Science Foundation under Grant No. 0932078000 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley California, during the Spring 2014 program on Algebraic Topology.

Received 9 April 2015

Accepted 27 January 2017

Published 5 July 2018