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

This paper incorporates the theory of Hochschild homology into our program on log motives. We discuss a geometric definition of logarithmic Hochschild homology of animated pre-log rings and construct an André-Quillen type spectral sequence. The latter degenerates for derived log smooth maps between...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2023-12, Vol.435, p.109354, Article 109354
Main Authors: Binda, Federico, Lundemo, Tommy, Park, Doosung, Østvær, Paul Arne
Format: Article
Language:English
Subjects:
Dividing covers
Logarithmic Hochschild homology
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Summary:This paper incorporates the theory of Hochschild homology into our program on log motives. We discuss a geometric definition of logarithmic Hochschild homology of animated 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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.109354