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.
A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology / F. Binda, T. Lundemo, D. Park, P.A. Oestvaer. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 435:(2023 Dec 15), pp. 109354.1-109354.66. [10.1016/j.aim.2023.109354]
A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology
F. BindaPrimo
;P.A. OestvaerUltimo
2023
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 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.File | Dimensione | Formato | |
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