THH and base-change for Galois extensions of ring spectra

Mathew, Akhil

doi:10.2140/agt.2017.17.693

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$\mathrm{THH}$ and base-change for Galois extensions of ring spectra

Akhil Mathew

Algebraic & Geometric Topology 17 (2017) 693–704

DOI: 10.2140/agt.2017.17.693

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 $THH (A) \otimes_{A} B \to THH (B)$ 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

Volume 17, issue 2 (2017)