Related papers: Hochster's type formulae

We provide a Hochster type formula for the local cohomology modules of binomial edge ideals. As a consequence we obtain a simple criterion for the Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford regularity and…

This first part of the paper describes the support of top graded local cohomology modules. As a corrolary one obtains a simple criteria for the vanishing of these modules and also the fact that they have finitely many minimal primes. The…

The Hilbert series of local cohomologies for monomial ideals, which are not necessarily square-free, is established. As applications, we give a sharp lower bound of the non-vanishing degree of local cohomologies and also a sharp lower bound…

We give a generalization of Hochster's formula for local cohomologies of square-free monomial ideals to monomial ideals, which are not necessarily square-free. Using this formula, we give combinatorial characterizations of generalized…

We give a combinatorial description of local cohomology modules of a graded module over a semigroup ring, with support at the graded maximal ideal. This combinatorial framework yields Hochster-type formulas for the Hilbert series of such…

Our main goal in this paper is to answer new positive cases of the natural generalized version of Hartshorne's celebrated question on cofiniteness of local cohomology modules, and consequently of Huneke's conjecture on the finiteness of…

A "squarefree module" over a polynomial ring $S = k[x_1, .., x_n]$ is a generalization of a Stanley-Reisner ring, and allows us to apply homological methods to the study of monomial ideals systematically. Let $Sq$ be the category of…

In this paper, some results on vanishing and non-vanishing of generalized local cohomology modules are presented and some relations between those modules and, Ext and ordinary local cohomology modules are studied. Also, several cofiniteness…

We discuss proofs of local cohomology theorems for topological modular forms, based on Mahowald-Rezk duality and on Gorenstein duality, and then make the associated local cohomology spectral sequences explicit, including their differential…

Assuming everywhere good reduction we generalize the class number formula of Taelman to Drinfeld modules over arbitrary coefficient rings. In order to prove this formula we develop a theory of shtukas and their cohomology.

Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the…

We construct an example where a local cohomology module of a hypersurface has p-torsion elements for every prime integer p, and consequently has infinitely many associated prime ideals. We also answer a related question of Hochster.

Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. Here, we show that, in the Serre subcategories of the category of $R$--modules, how the…

We study a question raised by Eisenbud, Mustata, and Stillman regarding the injectivity of natural maps from Ext modules to local cohomology modules. We obtain some positive answers to this question which extend earlier results of…

Some affirmative answers are given to Huneke's problems. The calculation of local cohomology modules with respect to an arbitrary pair of ideals $I,J$ can be reduced to calculation of local cohomology modules with respect to a pair of…

We introduce the notion of E-depth of graded modules over polynomial rings to measure the depth of certain Ext modules. First, we characterize graded modules over polynomial rings with (sufficiently) large E-depth as those modules whose…

Let $A$ be a noetherian ring, $\fa$ an ideal of $A$, and $M$ an $A$--module. Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about…

Any finite simplicial complex K and a partition of the vertex set of K determines a canonical quotient space of the moment-angle complex of K. We prove that the cohomology groups of such a space can be computed via some Hochster's type…

The main focus is the generic freeness of local cohomology modules in a graded setting. The present approach takes place in a quite nonrestrictive setting, by solely assuming that the ground coefficient ring is Noetherian. Under additional…

We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…