Binomial behavior of Betti numbers for modules of finite length

Abstract

The problem which we address in this article is that of providing bounds for the Betti numbers of modules M of finite length over a regular local ring (R,m,k) of dimension n. The conjectured lower bound is that the /th Betti number βi{M), or β*{M) if we wish to call attention to the ring R, is at least (). We establish this inequality for finite length modules of monomial type (see definition below).