A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology

Binda, Federico; Lundemo, Tommy; Park, Doosung; Østvær, Paul Arne

doi:10.1016/j.aim.2023.109354

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Logarithmic Ring Spectra1

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“…v n ] considered by Ausoni-Bayındır-Moulinos [ABM23]. In [BLPØ23b,Remark 9.8] we motivate the necessity of a theory of spectral log geometry. In analogy with the theory developed in [Lur18], we expect that the results of this paper will serve as an important technical tool for the development of such a theory.…”

Section: 11mentioning

confidence: 99%

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On the relationship between logarithmic TAQ and logarithmic THH

Lundemo

2021

Doc. Math.

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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.

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Section: 11mentioning

confidence: 99%

“…We denote by PreLog the resulting category of pre-log ring spectra. The idea to use the Grothendieck construction in the following remark is based on a suggestion of an anonymous referee of the paper [BLPØ23b].…”

Section: Logarithmic Ring Spectramentioning

confidence: 99%

On the relationship between logarithmic TAQ and logarithmic THH

Lundemo

2021

Doc. Math.

View full text Add to dashboard Cite

show abstract

A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology

Cited by 1 publication

References 32 publications

On the relationship between logarithmic TAQ and logarithmic THH

On the relationship between logarithmic TAQ and logarithmic THH

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