Let R be a commutative noetherian local ring R with maximal ideal m and
residue field k = R=m. The size of a minimal free resolution of a finite R-
module M is given by its Betti numbers fiRn(M) = rankk Ext*R(M, k). Dually,
that of a minimal injective resolution is measured by the Bass numbers
~nR(M) = rankk Ext*R(k, M).
These sizes may be estimated asymptotically on a natural, a polynomial,