Betti numbers of almost complete intersections

Abstract:

This paper produces some lower bounds on the betti numbers of cyclic modules R/I, where R is a commutative ring and I is an almost complete intersection. One particular result is that if R is a regular, local ring and R/I has finite length over R, then the sum of the betti numbers of R/I is at least 2^(dim R). This has been conjectured for arbitrary finite length modules over regular rings, but is still wide open (even for rings of dimension 5, the last I checked).

• Dvi file , Illinois J. Math. vol. 44, #3 (2000), 531-541.