Algebraic & Geometric Topology

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

Akhil Mathew

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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.

Article information

Algebr. Geom. Topol., Volume 17, Number 2 (2017), 693-704.

Received: 30 January 2015
Revised: 25 June 2016
Accepted: 9 July 2016
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
Secondary: 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 55P42: Stable homotopy theory, spectra

topological Hochschild homology Galois extensions structured ring spectra


Mathew, Akhil. $\mathrm{THH}$ and base-change for Galois extensions of ring spectra. Algebr. Geom. Topol. 17 (2017), no. 2, 693--704. doi:10.2140/agt.2017.17.693.

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