THE POINCARE-SERIES OF EVERY FINITELY GENERATED MODULE OVER A CODIMENSION 4 ALMOST COMPLETE INTERSECTION IS A RATIONAL-FUNCTION

[摘要] 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 Poincare series P(A)M(z) = SIGMA(i=0)infinity dim(k) Tor(i)A (M,k)z(i) is a rotational 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.

[发布日期] 1994-08-29