Binomial behavior of Betti numbers for modules of finite length

Edward Graham Evans, Jr. and Phillip Alan Griffith

Vol. 133 (1988), No. 2, 267–276

DOI: 10.2140/pjm.1988.133.267

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 i-th Betti number β_i(M), or β_i^R(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).

Mathematical Subject Classification 2000

Primary: 13C99

Secondary: 13D99, 13H05

Milestones

Received: 24 October 1986

Published: 1 June 1988