On The Annihilators of Derived Functors of Local Cohomology Modules and Finiteness Dimension

2013 ◽  
Vol 41 (1) ◽  
pp. 215-225
Author(s):  
K. Khashyarmanesh ◽  
F. Khosh-Ahang
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Derived Functors ◽  
Cohomology Modules

scholarly journals Proregular sequences, local cohomology, and completion

2003 ◽  
Vol 92 (2) ◽  
pp. 161 ◽  
Author(s):  
Peter Schenzel
Keyword(s):  
Noetherian Ring ◽  
Local Cohomology ◽  
Čech Complex ◽  
Regular Sequences ◽  
Local Cohomology Modules ◽  
Derived Functors ◽  
Adic Completion ◽  
Cech Complex ◽  
Cohomology Modules ◽  
The Ideal

As a certain generalization of regular sequences there is an investigation of weakly proregular sequences. Let $M$ denote an arbitrary $R$-module. As the main result it is shown that a system of elements $\underline x$ with bounded torsion is a weakly proregular sequence if and only if the cohomology of the Čech complex $\check C_{\underline x} \otimes M$ is naturally isomorphic to the local cohomology modules $H_{\mathfrak a}^i(M)$ and if and only if the homology of the co-Čech complex $\mathrm{RHom} (\check C_{\underline x}, M)$ is naturally isomorphic to $\mathrm{L}_i \Lambda^{\mathfrak a}(M),$ the left derived functors of the $\mathfrak a$-adic completion, where $\mathfrak a$ denotes the ideal generated by the elements $\underline x$. This extends results known in the case of $R$ a Noetherian ring, where any system of elements forms a weakly proregular sequence of bounded torsion. Moreover, these statements correct results previously known in the literature for proregular sequences.

scholarly journals Notes on endomorphisms, local cohomology and completion

2021 ◽  
pp. 169-180
Author(s):  
Peter Schenzel
Keyword(s):  
Noetherian Ring ◽  
Local Cohomology ◽  
Local Cohomology Module ◽  
Finitely Generated Module ◽  
Content Type ◽  
Local Cohomology Modules ◽  
Derived Functors ◽  
Adic Completion ◽  
Cohomology Modules

Let M M denote a finitely generated module over a Noetherian ring R R . For an ideal I ⊂ R I \subset R there is a study of the endomorphisms of the local cohomology module H I g ( M ) , g = g r a d e ( I , M ) , H^g_I(M), g = grade(I,M), and related results. Another subject is the study of left derived functors of the I I -adic completion Λ i I ( H I g ( M ) ) \Lambda ^I_i(H^g_I(M)) , motivated by a characterization of Gorenstein rings given in [25]. This provides another Cohen-Macaulay criterion. The results are illustrated by several examples. There is also an extension to the case of homomorphisms of two different local cohomology modules.

Local Cohomology Modules, Serre Subcategories and Derived Functors of Torsion Functors

2012 ◽  
Vol 19 (spec01) ◽  
pp. 1187-1196 ◽  
Author(s):  
K. Khashyarmanesh ◽  
F. Khosh-Ahang
Keyword(s):  
Local Cohomology ◽  
Derived Functor ◽  
Regular Sequences ◽  
Serre Subcategory ◽  
Local Cohomology Modules ◽  
Derived Functors ◽  
Cohomology Modules ◽  
Exact Sequences ◽  
Serre Subcategories

In this research, by using filter regular sequences, we obtain some exact sequences of right or left derived functors of local cohomology modules. Then we use them to gain some conditions under which a right or left derived functor of some special functors over local cohomology modules belongs to a Serre subcategory. These results can conclude some generalizations of previous results in this context or regain some of them.

ON THE BEHAVIOR OF APPLYING DERIVED FUNCTORS OF TORSION FUNCTORS ON LOCAL COHOMOLOGY MODULES

2012 ◽  
Vol 11 (06) ◽  
pp. 1250113
Author(s):  
K. KHASHYARMANESH ◽  
F. KHOSH-AHANG
Keyword(s):  
Local Cohomology ◽  
Cohomological Dimension ◽  
Prime Ideals ◽  
Local Cohomology Modules ◽  
Associated Prime Ideals ◽  
Special Cases ◽  
Derived Functors ◽  
Cohomology Modules ◽  
Associated Prime

In this note, by using some properties of the local cohomology functors of weakly Laskerian modules, we study the behavior of right and left derived functors of torsion functors. In fact, firstly we gain some isomorphisms in the context of these functors, grade and cohomological dimension. Then we study their supports and their sets of associated prime ideals in special cases.

scholarly journals On derived functors of graded local cohomology modules—II

2020 ◽  
Vol 64 (4) ◽  
pp. 595-612
Author(s):  
Tony J. Puthenpurakal ◽  
Sudeshna Roy ◽  
Jyoti Singh
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Derived Functors ◽  
Cohomology Modules

scholarly journals Artinianness of local cohomology modules

2014 ◽  
Vol 52 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Moharram Aghapournahr ◽  
Leif Melkersson
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Cohomology Modules

On the associated primes of local cohomology modules

1999 ◽  
Vol 27 (12) ◽  
pp. 6191-6198 ◽  
Author(s):  
K. Khashyarmanesh ◽  
Sh Salarian
Keyword(s):  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Cohomology Modules

Some properties of local homology and local cohomology modules

2013 ◽  
Vol 50 (1) ◽  
pp. 129-141
Author(s):  
Tran Nam
Keyword(s):  
Local Cohomology ◽  
Local Homology ◽  
Local Cohomology Modules ◽  
Cohomology Modules ◽  
Compact Module

We study some properties of representable or I-stable local homology modules HiI (M) where M is a linearly compact module. By duality, we get some properties of good or at local cohomology modules HIi (M) of A. Grothendieck.

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