Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0709.1778

A local homology theory for linearly compact modules

Nguyen Tu Cuong·Tran Tuan Nam
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of A. Grothendieck. Some basic properties such as the noetherianness, the vanishing and non-vanishing of local homology modules of linearly compact modules are proved. A duality theory between local homology and local cohomology modules of linearly compact modules is developed by using Matlis duality and Macdonald duality. As consequences of the duality theorem we obtain some generalizations of well-known results in the theory of local cohomology for semi-discrete linearly compact modules.

Explore related subjects

math.ACmath.RA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nguyen Tu Cuong, Tran Tuan Nam. 2007-09-12. A local homology theory for linearly compact modules. https://arxiv.org/abs/0709.1778

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

$t$-Young complexes and squarefree powers of $t$-path ideals

We introduce a new class of simplicial complexes, called \emph{$t$-Young complexes}, arising from Young diagrams and a positive integer~$t$. We show that every $t$-Young complex is either contractible or homotopy equivalent to a wedge of spheres, and a complete characterization of their vertex-decomposability is provided. Interestingly, $t$-Young complexes naturally appear as the Alexander dual complexes of squarefree powers of $t$-path ideals of path graphs. For this family, we use generating functions to obtain an explicit formula for homotopy type. As applications, we determine the projective dimension and the Krull dimension of these squarefree powers.

math.AC↗
arXiv2026

Stanley-Reisner Theory in Mixed Characteristic

We discuss a class of mixed characteristic rings defined analogously to Stanley-Reisner rings by replacing one variable with a uniformizing parameter for a discrete valuation ring. We adapt Hochster's formula for Tor and Ext modules, Hochster's formula for local cohomology, and Terai's criterion for Serre conditions to this new setting; one of the tools needed is cellular sheaf cohomology, for which we give a brief treatment.

math.AC↗
arXiv2026

Hilbert Series and Logarithmic Degrees of $A$-Hypergeometric Series

Fix a generic weight vector and a fake exponent of a homogeneous $A$-hypergeometric system. Using all corresponding standard pairs, including embedded ones, we construct an Artinian quotient of the Stanley--Reisner ring of the link of the negative support. Its Hilbert series gives the graded dimensions of the orthogonal complement of the local fake indicial ideal and, under the Okuyama--Saito Frobenius condition, those of the leading logarithmic coefficient space of actual series solutions. The construction requires no Cohen--Macaulay hypothesis. When a top-dimensional standard pair occurs and the link is Cohen--Macaulay, the Hilbert series specializes to the $h$-polynomial of the link.

math.AC↗