1998/09/29 by Bernhard Köck, Köck, Bernhard
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #Topological and Geometric Data Analysis #math.AC #math.AG #math.KT #math.RA
paper · pdf · doi:10.48550/arxiv.math/9809175
35 pages
openalex publication_date 1998/09/29 · arxiv created 1999/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a commutative ring and I an ideal in R which is locally generated by a regular sequence of length d. Then, each projective R/I-module V has an R-projective resolution P. of length d. In this paper, we compute the homology of the n-th Koszul complex associated with the homomorphism P1 --> P0 for all n, if d = 1. This computation yields a new proof of the classical Adams-Riemann-Roch formula for regular closed immersions which does not use the deformation to the normal cone any longer. Furthermore, if d = 2, we compute the homology of the complex N Sym2 K(P.) where K and N denote the functors occurring in the Dold-Kan correspondence.