Asymptotic Behaviour and Artinian Property of Graded Local Cohomology Modules

Hassanzadeh, Seyed Hamid; Jahangiri, Maryam; Zakeri, H.

doi:10.1080/00927870902828843

Cited by 6 publications

(9 citation statements)

References 9 publications

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“…1 and p 2 ∈ Ass M 2 , iii) every cyclic submodule of M is pure, iv) M = S/I where I is a monomial ideal. We believe that the question has negative answer for dimension 4. Until now we are not succeed to find such a counterexample.…”

Section: Introductionmentioning

confidence: 86%

Relative Cohen-Macaulayness and relative unmixedness of bigraded modules

Jahangiri¹,

Rahimi²

2012

J. Commut. Algebra

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Section: Introductionmentioning

confidence: 86%

Relative Cohen-Macaulayness and relative unmixedness of bigraded modules

Jahangiri¹,

Rahimi²

2012

J. Commut. Algebra

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“…In [6] it is shown: If f = c, then depth(a 0 , H c R + (M ) n ) is asymptotically stable for n → −∞.…”

Section: Proof According To [2 Proposition 35] the Set Assmentioning

confidence: 99%

Asymptotic depth of twisted higher direct image sheaves

Bär

Brodmann

2008

Proc. Amer. Math. Soc.

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Let π : X → X 0 be a projective morphism of schemes, such that X 0 is noetherian and essentially of finite type over a field K. Let i ∈ N 0 , let F be a coherent sheaf of O X -modules and let L be an ample invertible sheaf over X. Let Z 0 ⊆ X 0 be a closed set. We show that the depth of the higher direct image sheafThere are various examples which show that the mentioned asymptotic stability may fail if dim(X 0 ) ≥ 3. To prove our stability result, we show that for a finitely generated graded module M over a homogeneous noetherian ring R = n≥0 R n for which R 0 is essentially of finite type over a field and an ideal a 0 ⊆ R 0 the a 0 -depth of the n-th graded component H i R+ (M ) n of the i-th local cohomology module of M with respect to R + := k>0 R k ultimately becomes constant in codimension ≤ 2 if n tends to −∞.

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“…The asymptotic behavior of the components H i R + (M) n when n → −∞ has been studied by many authors, too. See for example [1], [2], [5] and [12]. But, we know not much about the graded components H i a (M) n where a is an arbitrary homogeneous ideal of R. Although, there are some studies in this topic, see for example [4], [10] and [16].…”

Section: Introductionmentioning

confidence: 99%

“…Also, a graded R-module N = n∈Z N n is said to be tame if {n ∈ Z|N n = 0 and N n+1 = 0} is a finite set. Tameness of local cohomology modules is one of the most fundamental concepts concerning this modules and attracts lots of interests, see for example [1], [2], [4], [5] and [18]. In [5, 2.2], the authors show that…”

Section: Introductionmentioning

confidence: 99%

Graded local cohomology modules with respect to the linked ideals

Jahangiri¹,

Nadali²,

Sayyari³

2021

Preprint

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Let R = ⊕ n∈N0 R n be a standard graded ring, M be a finitely generated graded R-module and R + := ⊕ n∈N R n denotes the irrelevant ideal of R. In this paper, considering the new concept of linkage of ideals over a module, we study the graded components H i a (M ) n when a is an h-linked ideal over M . More precisely, we show that H i a (M ) is tame in each of the following cases:(i) i = f R+ a (M ), the first integer i for which R + 0 : H i a (M ); (ii) i = cd(R + , M ), the last integer i for which H i R+ (M ) = 0, and a = b + R + where b is an h-linked ideal with R + over M . Also, among other things, we describe the components H i a (M ) n where a is radically h-Mlicci with respect to R + of length 2.

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Asymptotic Behaviour and Artinian Property of Graded Local Cohomology Modules

Cited by 6 publications

References 9 publications

Relative Cohen-Macaulayness and relative unmixedness of bigraded modules

Relative Cohen-Macaulayness and relative unmixedness of bigraded modules

Asymptotic depth of twisted higher direct image sheaves

Graded local cohomology modules with respect to the linked ideals

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