Lundemo, Tommy

On the relationship between logarithmic TAQ and logarithmic THH

Doc. Math. 26, 1187-1236 (2021)
DOI: 10.25537/dm.2021v26.1187-1236
Communicated by Mike Hill

Summary

We provide a new description of logarithmic topological André-Quillen homology in terms of the indecomposables of an augmented ring spectrum. The new description allows us to interpret logarithmic TAQ as an abstract cotangent complex, and leads to a base-change formula for logarithmic topological Hochschild homology. The latter is analogous to results of Weibel-Geller for Hochschild homology of discrete rings, and of McCarthy-Minasian and Mathew for topological Hochschild homology. For example, our results imply that logarithmic THH satisfies base-change for tamely ramified extensions of discrete valuation rings.

Mathematics Subject Classification

55P43, 14F10, 19D55

Keywords/Phrases

topological Hochschild homology, topological André-Quillen homology, logarithmic structures

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Affiliation

Lundemo, Tommy
IMAPP, Radboud University Nijmegen, The Netherlands

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