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https://www.sciencedirect.com/science/article/abs/pii/S0021869308001099
We examine the question of whether the support of an arbitrary local cohomology module of a finitely generated module over a Noetherian ring with supp…
https://en.wikipedia.org/wiki/Local_cohomology
Definition. In the geometric form of the theory, sections γ Y are considered of a sheaf F of abelian groups, on a topological space X, with support in a closed subset Y. The derived functors of γ Y form local cohomology groups For applications in commutative algebra, the space X is the spectrum Spec( R) of a commutative ring R...
https://www.researchgate.net/publication/251410362_On_the_support_of_local_cohomology
This is equivalent to ask whether the support of local cohomology modules of Noetherian rings (or modules) must be Zariski-closed subsets of Spec R. Recently Huneke, Katz and Marley [9] and later ...
https://www.sciencedirect.com/science/article/pii/S0021869308001099
Nov 01, 2009 · Rotthaus and Sega [21] proved that the support of the top local cohomology of the irrelevant ideal is always closed in a standard graded Noetherian ring. 3 Katzman, in an argument attributed to G. Lyubeznik, proves that if R is a ring of positive prime characteristic and I is an ideal generated by n elements, then the support of H n I (R) is ...Cited by: 20
https://www.researchgate.net/publication/327032863_On_the_support_of_local_and_formal_cohomology
In the process, we compute the local cohomology of rings of polynomials with integer coefficients---supported at generic determinantal ideals---and also obtain results on F-modules and D-modules ...
https://academic.oup.com/imrn/article-abstract/2018/23/7137/3836905
May 19, 2017 · Finally, in Section 7 we turn our attention to hypersurfaces and describe the support of their local cohomology modules, which turn out to be closed. (The fact that the support is closed was simultaneously and independently also discovered by Mel Hochster and Luis Núñez-Betancourt in [ 6 ] using a different method.)Cited by: 2
http://www.math.lsa.umich.edu/~hochster/SuppLocCohMRL.pdf
In this paper, we study the support of local cohomology modules over a ring of positive characteristic. We investigate the structure of Hi I pRqas an RxFy-module. Using this technique we recover several results previously known for top local cohomology, regular rings, and rings of small dimension (see Corollaries4.6, 4.10, and4.14).
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.541.1917
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Dedicated to Professor Paul Roberts on the occasion of his sixtieth birthday. Abstract. We examine the question of whether the support of an arbitrary local coho-mology module of a finitely generated module over a Noetherian ring with support in a given ideal must be closed in the Zariski topology.
http://www.math.uic.edu/~bshipley/huneke.pdf
domains.1 Local cohomology has since become an indepensable tool and is the subject of much research. This article will be concentrating on several applications of local cohomology, whose proofs force the development of most of the basic material concerning local cohomology. All rings in this
https://www.msri.org/~de/papers/pdfs/2000-002.pdf
Cohomology on Toric Varieties and Local Cohomology with Monomial Supports DAVID EISENBUDyx, MIRCEA MUSTAT˘A y{AND MIKE STILLMANzk yDepartment of Mathematics, University of California, Berkeley, CA 94720, U.S.A. zDepartment of Mathematics, Cornell University, Ithaca, NY …
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