Related papers: Global parameter test ideals

Inspired by Jorgensen et. al., it is proved that if a Cohen--Macaulay local ring $R$ with dualizing module admits a suitable chain of semidualizing $R$--modules of length $n$, then $R\cong Q/(I_1+\cdots+I_n)$ for some Gorenstein ring $Q$…

Tight closure test ideals have been central to the classification of singularities in rings of characteristic $p>0$, and via reduction to characteristic $p$, in equal characteristic zero as well. A summary of their properties and…

Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H^{d-1}_{I,J}(M)$ are computed by means of the…

In this work we describe the local cohomology of reflexive modules of rank one over normal semigroup rings with respect to monomial ideals. Using our description we show that the problem of classifying maximal Cohen-Macaulay modules of rank…

The purpose of this paper is to give affirmative answers to two open questions as follows. Let $(R, \m)$ be a generalized Cohen-Macaulay Noetherian local ring. Both questions, the first question was raised by M. Rogers \cite {R} and the…

Given a Cohen-Macaulay local ring, the cohomology annihilator ideal and the annihilator of the stable category of maximal Cohen-Macaulay modules are two ideals closely related both with each other and the singularities of the ring. Kimura…

We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings which have finite $F$-representation type after localization and completion at every prime ideal. As applications, we show that if $R$ is such…

We study stable trace ideals in one dimensional local Cohen-Macaulay rings and give numerous applications.

Let $M$ be a finitely generated module of dimension $d$ over a Noetherian local ring $(R,\m)$ and $\q $ the parameter ideal generated by a system of parameters $\x = (x_1,..., x_d)$ of $M$. For each positive integer $n$, set…

An ideal I of a local Cohen-Macaulay ring R is called a cohomologically complete intersection if H^i_I(R) = 0 for all i \neq c = height(I). Here H^i_I(R), i \in Z denotes the local cohomology of R with respect to I. For instance, a…

Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite R-module. It is shown that, if (R;m) is a complete local ring, then under certain conditions a contains a regular element on DR(Hc a(M)), where c = cd(a;M). A…

This paper applies G. Lyubeznik's notion of $F$-finite modules to describe in a very down-to-earth manner certain annihilator submodules of some top local cohomology modules over Gorenstein rings. As a consequence we obtain an explicit…

The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…

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…

Thirty years ago, Huneke (for local rings) and Lyubeznik (in general) conjectured that for all regular rings $R$, the local cohomology modules $H^i_I(R)$ have finitely many associated prime ideals. We prove substantial new cases of their…

The aim of this paper is to study a deep connection between local cohomology annihilators and Macaulayfication and arithmetic Macaulayfication over a local ring. Local cohomology annihilators appear through the notion of p-standard system…

For a Cohen-Macaulay local ring $(R,\mathfrak{m})$ with canonical module, we study how relations between $\text{index}(R)$ and $\text{g}\ell\ell(R)$ and between $\text{index}(R)$ and $e(R)$ are preserved when factoring out regular sequences…

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…

Let $R$ be a noetherian ring, $\fa$ an ideal of $R$ such that $\dim R/\fa=1$ and $M$ a finite $R$--module. We will study cofiniteness and some other properties of the local cohomology modules $\lc^{i}_{\fa}(M)$. For an arbitrary ideal $\fa$…

In this paper, we show examples of local cohomology modules over ramified regular local ring, having finite set of associated primes. In doing so we consider our ramified regular local ring as Eisenstein extension of an unramified regular…