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arXiv · 2209.14182

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

Federico Binda·Tommy Lundemo·Doosung Park·Paul Arne Østvær
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Abstract

This paper incorporates the theory of Hochschild homology into our program on log motives. We discuss a geometric definition of logarithmic Hochschild homology of derived pre-log rings and construct an André-Quillen type spectral sequence. The latter degenerates for derived log smooth maps between discrete pre-log rings. We employ this to show a logarithmic version of the Hochschild-Kostant-Rosenberg theorem and that logarithmic Hochschild homology is representable in the category of log motives. Among the applications, we deduce a generalized residue sequence involving blow-ups of log schemes.

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Federico Binda, Tommy Lundemo, Doosung Park, Paul Arne Østvær. 2023-10-06. A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology. https://arxiv.org/abs/2209.14182

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