scholarly journals Degree bounds for generators of cohomology modules and Castelnuovo-Mumford regularity

1998 ◽  
Vol 152 ◽  
pp. 153-174 ◽  
Author(s):  
Uwe Nagel ◽  
Peter Schenzel
Keyword(s):  
Local Cohomology ◽  
Degree Bounds ◽  
Local Cohomology Modules ◽  
Cohomology Modules

Abstract.By extending Mumford’s result on the generating by global sections there are estimates on the degree for generators of local cohomology modules. These arguments provide bounds on the Castelnuovo-Mumford regularity, in particular for Cohen-Macaulay varieties. As an application they imply a few more cases of varieties that satisfy a conjecture posed by Eisenbud and Gôto.

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.

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.

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