#### Volume 17, issue 2 (2017)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
$\mathrm{THH}$ and base-change for Galois extensions of ring spectra

### Akhil Mathew

Algebraic & Geometric Topology 17 (2017) 693–704
##### Abstract

We treat the question of base-change in $THH$ for faithful Galois extensions of ring spectra in the sense of Rognes. Given a faithful Galois extension $A\to B$ of ring spectra, we consider whether the map $THH\left(A\right){\otimes }_{A}B\to THH\left(B\right)$ is an equivalence. We reprove and extend positive results of Weibel and Geller, and McCarthy and Minasian, and offer new examples of Galois extensions for which base-change holds. We also provide a counterexample where base-change fails.

##### Keywords
topological Hochschild homology, Galois extensions, structured ring spectra
##### Mathematical Subject Classification 2010
Primary: 55P43
Secondary: 13D03, 55P42
##### Publication
Received: 30 January 2015
Revised: 25 June 2016
Accepted: 9 July 2016
Published: 14 March 2017
##### Authors
 Akhil Mathew Department of Mathematics Harvard University 1 Oxford Street Cambridge, MA 02138 United States