2022/09/28 by Federico Binda, Tommy Lundemo, Binda, Federico +5 · 2 citations
Mathematics · #13D03 #14A21 #14F42 #19D55 #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2209.14182
openalex publication_date 2022/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.