On the relationship between logarithmic TAQ and logarithmic THH
Abstract
We provide a new description of logarithmic topological Andr\'e-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 an 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.
Cite
@article{arxiv.2004.03524,
title = {On the relationship between logarithmic TAQ and logarithmic THH},
author = {Tommy Lundemo},
journal= {arXiv preprint arXiv:2004.03524},
year = {2021}
}
Comments
37 pages. Added a section on base-change for log THH for tamely ramified extensions of DVRs and various other minor updates. Accepted for publication in Documenta Mathematica