Symmetric powers of complete modules over a two-dimensional regular local ring

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

On the value-semigroup of a simple complete ideal in a two-dimensional regular local ring

Let R be a two-dimensional regular local ring with maximal ideal m, and let ℘ be a simple complete m-primary ideal which is residually rational. Let R0 := R $ R1 $ · · · $ Rr be the quadratic sequence associated to ℘, let Γ℘ be the value-semigroup associated to ℘, and let (ej(℘))0≤j≤r be the multiplicity sequence of ℘. We associate to ℘ a sequence (γi(℘))0≤i≤g of natural integers which we call ...

The Cohomology of Modules over a Complete Intersection Ring

We investigate the cohomology of modules over commutative complete intersection rings. The first main result is that if M is an arbitrary module over a complete intersection ring R, and if Ext 2n R (M, M) = 0 for some n ≥ 1 then M has finite projective dimension. The second main result gives a new proof of the fact that the support variety of a Cohen-Macaulay module whose completion is indecomp...

The Leading Ideal of a Complete Intersection of Height Two in a 2-dimensional Regular Local Ring

Let (S,n) be a 2-dimensional regular local ring and let I = (f, g) be an ideal in S generated by a regular sequence f, g of length two. Let I∗ be the leading ideal of I in the associated graded ring grn(S), and set R = S/I and m = n/I. In [GHK2], we prove that if μG(I ∗) = n, then I∗ contains a homogeneous system {ξi}1≤i≤n of generators such that deg ξi + 2 ≤ deg ξi+1 for 2 ≤ i ≤ n−1, and htG(ξ...

rigid resolution of a finitely generated module over a regular local ring