Title

The Poincaré series of every finitely generated module over a codimension four almost complete intersection is a rational function

Abstract

Let (R, M, k) be a regular local ring in which two is a unit and let A = R/J, where J is a five generated grade four perfect ideal in R. We prove that the Poincaré series PMA(z) = Σ∞i=0 dimk TorAi(M, k)zi is a rational function for all finitely generated A-modules M. We also prove that the Eisenbud conjecture holds for A, that is, if M is an A-module whose Betti numbers are bounded, then the minimal resolution of M by free A-modules is eventually periodic of period at most two.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/0022-4049(94)90062-0

Publication Date

8-29-1994

Journal Title

Journal of Pure and Applied Algebra

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