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$\mathrm{THH}$ 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 B of ring spectra, we consider whether the map THH(A) AB THH(B) 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
References
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