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Some results on Artinian cofinite top local cohomology modules

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0 Published in 2018 at "Archiv der Mathematik"

DOI: 10.1007/s00013-018-1250-5

Abstract: Let $$(R,\mathfrak {m})$$(R,m) be a Noetherian local ring, I be an ideal of R, and M be a finitely generated R-module such that $${\text {H}}_I^t(M)$$HIt(M) is Artinian and I-cofinite, where $$t={\text {cd}}\,(I,M)$$t=cd(I,M). In this paper,… read more here.

Keywords: top local; results artinian; artinian cofinite; local cohomology ... See more keywords

Decomposition of graded local cohomology tables

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0 Published in 2018 at "Mathematische Zeitschrift"

DOI: 10.1007/s00209-020-02494-9

Abstract: Let R be a polynomial ring over a field. We describe the extremal rays and the facets of the cone of local cohomology tables of finitely generated graded R -modules of dimension at most two.… read more here.

Keywords: local cohomology; decomposition graded; graded local; cohomology tables ... See more keywords

Cofiniteness of Local Cohomology Modules over Homomorphic Image of Cohen-Macaulay Rings

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0 Published in 2018 at "Acta Mathematica Vietnamica"

DOI: 10.1007/s40306-018-0246-3

Abstract: AbstractLet (R,????)$(R,\mathfrak {m})$ be a Noetherian local ring, M a non-zero finitely generated R-module, and let I be an ideal of R. In this paper, we establish some new properties of local cohomology modules HIi(M)$\mathrm… read more here.

Keywords: homomorphic image; local cohomology; modules homomorphic; cohomology modules ... See more keywords

Local cohomology modules via certain flat extension rings

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0 Published in 2018 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.01.045

Abstract: Abstract Let ( R , m ) be a Noetherian local ring and M a finitely generated R-module. Let P ∈ Spec ( R ˆ ) and p = P ∩ R . Then the… read more here.

Keywords: modules via; local cohomology; via certain; cohomology modules ... See more keywords

Lyubeznik numbers for Pfaffian rings

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1 Published in 2020 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2019.106247

Abstract: We study the structure of local cohomology with support in Pfaffian varieties as a module over the Weyl algebra D_X of differential operators on the space X of n x n complex skew-symmetric matrices. The… read more here.

Keywords: numbers pfaffian; lyubeznik numbers; local cohomology; pfaffian rings ... See more keywords

FROBENIUS ACTIONS ON LOCAL COHOMOLOGY MODULES AND DEFORMATION

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1 Published in 2017 at "Nagoya Mathematical Journal"

DOI: 10.1017/nmj.2017.20

Abstract: Let $(R,\mathfrak{m})$ be a Noetherian local ring of characteristic $p>0$ . We introduce and study $F$ -full and $F$ -anti-nilpotent singularities, both are defined in terms of the Frobenius actions on the local cohomology modules… read more here.

Keywords: frobenius actions; local cohomology; modules deformation; cohomology modules ... See more keywords

On the cofiniteness of generalized local cohomology modules with respect to the class of modules in dimension less than a fixed integer

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1 Published in 2021 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1897831

Abstract: Abstract Let n and t be non-negative integers, R a commutative Noetherian ring with an ideal of R, M and N finite R-modules, and X an arbitrary R-module. We prove that if is an R-module… read more here.

Keywords: modules respect; module; local cohomology; generalized local ... See more keywords

The first non-isomorphic local cohomology modules with respect to their ideals

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0 Published in 2018 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498818502304

Abstract: Let [Formula: see text] be ideals of a commutative Noetherian ring [Formula: see text] and [Formula: see text] be a finitely generated [Formula: see text]-module. By using filter regular sequences, we show that the infimum… read more here.

Keywords: local cohomology; see text; formula see; cohomology modules ... See more keywords

Some splitting theorems for local cohomology modules with respect to a pair of ideals

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1 Published in 2019 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498821500158

Abstract: Suppose that R is a commutative ring with identity, I, J are ideals of R, and let M be a finitely generated R-module. Let HI,Ji(−) be the ith local cohomology functor with respect to (I,J).… read more here.

Keywords: theorems local; splitting theorems; modules respect; local cohomology ... See more keywords

Annihilator of top Local Cohomology and Lynch's Conjecture

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1 Published in 2022 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498824502001

Abstract: Let $R$ be a commutative Noetherian ring, $\mathfrak a$ a proper ideal of $R$ and $N$ a nonzero finitely generated $R$-module with $N\neq \mathfrak a N$. Let $c$ be the greatest nonnegative integer $i$ such… read more here.

Keywords: annihilator top; local cohomology; lynch conjecture; top local ... See more keywords

On the Finiteness Results of Generalized Local Cohomology Modules with Respect to a Pair of Ideals

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1 Published in 2017 at "Taiwanese Journal of Mathematics"

DOI: 10.11650/tjm/8112

Abstract: We study the finiteness of associated primes and support of the generalized local cohomology modules H I,J(M,N) concerning Grothendieck’s conjecture and Huneke’s question. The paper also discusses the relationship between the vanishing and the finiteness… read more here.

Keywords: finiteness results; local cohomology; results generalized; generalized local ... See more keywords