Content of local cohomology, parameter ideals, and robust algebras

Local Cohomology at Monomial Ideals

Serre Subcategories and Local Cohomology Modules with Respect to a Pair of Ideals

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

Ideals with Maximal Local Cohomology Modules

This paper finds its motivation in the pursuit of ideals whose local cohomology modules have maximal Hilbert functions. In [8], [9] we proved that the lexicographic (resp. squarefree lexicographic) ideal of a family of graded (resp. squarefree) ideals with assigned Hilbert function provides sharp upper bounds for the local cohomology modules of any of the ideals of the family. Moreover these bo...

Free Resolutions of Parameter Ideals for Some Rings with Finite Local Cohomology

Let R be a d-dimensional local ring, with maximal ideal m, containing a field and let x1, . . . , xd be a system of parameters for R. If depthR ≥ d − 1 and the local cohomology module H m (R) is finitely generated, then there exists an integer n such that the modules R/(x 1 , . . . , x d ) have the same Betti numbers, for all i ≥ n.

0 Local cohomology , arrangements of subspaces and monomial ideals

If k is the field of complex numbers (or, more generally, a field of characteristic zero), the module H i I(R) is known to have a module structure over the Weyl algebra An(k), and one can therefore consider its characteristic cycle, denoted CC(H i I(R)) in this paper (see e.g. [2, I.1.8.5]). On the other hand, the arrangement X defines a partially ordered set P (X) whose elements correspond to ...