Algebraic & Geometric Topology

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

Akhil Mathew

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1508431440

Digital Object Identifier
doi:10.2140/agt.2017.17.693

Mathematical Reviews number (MathSciNet)
MR3623668

Zentralblatt MATH identifier
1370.55002

Subjects
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

Keywords
topological Hochschild homology Galois extensions structured ring spectra

Citation

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. https://projecteuclid.org/euclid.agt/1508431440


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