### Computing the homology of Koszul complexes, by Bernhard Koeck

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 P_1 --> P_0 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 Sym^2 K(P.) where K and N denote the functors
occurring in the Dold-Kan correspondence.

Bernhard Koeck <Bernhard.Koeck@math.uni-karlsruhe.de>