On Local-to-global Spectral Sequences for the Cohomology of Diagrams

On Reducing sequences and an Application to Local Cohomology Modules

Local-to-global Spectral Sequences for the Cohomology of Diagrams

The cohomology of diagrams arises as a natural object of study in several mathematical contexts: in deformation theory (see [GS2, GS1, GGS]), and in classifying diagrams of groups, as in [C]. If I is the one-object category corresponding to a group G, a diagram X ∈ C is just an object in C equipped with a G-action, and its cohomology is the equivariant cohomology of [I] (cf. [P1, §2]). On the o...

On natural homomorphisms of local cohomology modules

‎Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$‎. ‎Let $I$ be an ideal of $R$ with $grade(I,M)=c$‎. ‎In this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎The main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎Tor^{R}_c(k,H^c_I(M))to kotim...

On the Associated Primes of the generalized $d$-Local Cohomology Modules

The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary  generalized local cohomology  modules.  Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$  are  finitely generated  $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...

ON GRADED LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...