Graded Local Cohomology Modules and Their Associated Primes

Lim, Chia S.

doi:10.1081/agb-120027926

Cited by 5 publications

(3 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But R is also Cohen-Macaulay by hypothesis, so dim M p = dim R p /I p = dim R p − htI p . By [L,Lemma 1.2.2], all minimal primes of I have the same height, so that, htI p = htI for each p. By combining the above arguments, we obtain…”

Section: Top Local Cohomologymentioning

confidence: 89%

See 1 more Smart Citation

Graded version of local cohomology with respect to a pair of ideals

Lima¹,

Pérez²

2017

J. Commut. Algebra

View full text Add to dashboard Cite

In this paper, we prove some well-known results on local cohomology with respect to a pair of ideals in graded version, such as, Independence Theorem, Lichtenbaum-Harshorne Vanishing Theorem, Basic Finiteness and Vanishing Theorem, among others. Besides, we present a generalized version of Melkersson Theorem about Artinianess of modules and a result concerning Artinianess of local cohomology modules.

show abstract

Section: Top Local Cohomologymentioning

confidence: 89%

“…Throughout this section we assume R and M are as in section 3. In particular, ht(R [L,Lemma 1.2.2], all minimal primes of I have the same height, so that, htI p = htI for each p. By combining the above arguments, we obtain…”

Section: Top Local Cohomologymentioning

confidence: 95%

Graded version of local cohomology with respect to a pair of ideals

Lima¹,

Pérez²

2017

J. Commut. Algebra

View full text Add to dashboard Cite

show abstract

“…In the special case where R and M are both CM this is shown in [10]. Under additional mild restrictions on R 0 , we get the requested "local" extension of (1.4) to the case dim(R 0 ) = 2, namely (cf.…”

Section: Introductionmentioning

confidence: 92%

Low-codimensional associated primes of graded components of local cohomology modules

2004

View full text Add to dashboard Cite

Let R = n 0 R n be a homogeneous noetherian ring and let M be a finitely generated graded R-module. Let H i R + (M) denote the ith local cohomology module of M with respect to the irrelevant ideal R + := n>0 R n of R. We show that if R 0 is a domain, there is some s ∈ R 0 \{0} such that the (R 0 ) s -modules H i R + (M) s are torsion-free (or vanishing) for all i. On use of this, we can deduce the following results on the asymptotic behaviour of the nth graded component H i R + (M) n of H i R + (M) for n → −∞: if R 0 is a domain or essentially of finite type over a field, the set {p 0 ∈ Ass R 0 (H i R + (M) n ) | height(p 0 ) 1} is asymptotically stable for n → −∞. If R 0 is semilocal and of dimension 2, the modules H i R + (M) are tame. If R 0 is in addition a domain or essentially of finite type over a field, the set Ass R 0 (H i R + (M) n ) is asymptotically stable for n → −∞.  2004 Elsevier Inc. All rights reserved.

show abstract

On the asymptotic behaviour of associated primes of generalized local cohomology modules

Khashyarmaneshs

Abbasi²

2007

J. Aust. Math. Soc.

View full text Add to dashboard Cite

Let M and A' be finitely generated and graded modules over a standard positive graded commutative Noetherian ring R, with irrelevant ideal /?+. Let H# (M, N) n be the nth component of the graded generalized local cohomology module H R+ (M, N). In this paper we study the asymptotic behavior of Assfl + (//| + (Af, N) n ) as n ->• -oo whenever k is the least integer j for which the ordinary local cohomology module H' R+ (N) is not finitely generated.

show abstract

Graded Local Cohomology Modules and Their Associated Primes

Cited by 5 publications

References 5 publications

Graded version of local cohomology with respect to a pair of ideals

Graded version of local cohomology with respect to a pair of ideals

Low-codimensional associated primes of graded components of local cohomology modules

On the asymptotic behaviour of associated primes of generalized local cohomology modules

Contact Info

Product

Resources

About