Associated primes of local cohomology modules

By K. Divaani-Aazar, A. Mafi. 2004

129 citations recorded by the source corpus.

Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. Let t be a natural integer. It is shown that there is a finite subset X of Spec R, such that Ass R (H t a (M)) is contained in X union with the union of the sets Ass R (Ext j R (R/a, H i a (M))), where 0 ≤ i < t and 0 < j ≤ t 2 + 1. As an immediate consequence, we deduce that the first non-α-cofinite local cohomology module of M with respect to a has only finitely many associated prime ideals.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/30623126706c98940d9cfb7e55c4387893cbab91

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Associated primes of local cohomology modules and of Frobenius powers (2004, background): “If i is the smallest integer for which Ha(M) is not a finitely generated R-module, then the set Ass H i a(M) is finite, as proved in [3, 20].”
Associated primes and cofiniteness of local cohomology modules (2004, methodology): “a(M)) → Ext1 R(R/a,M/Γa(M)). Since the left side is zero and the right side is ﬁnite we get the result. The next result has been shown, using a spectral sequence argument, by Divaani-Aazar and Maﬁ in [DiM]. Corollary 2.3 Let M be an R-module with Exti R(R/a,M) is ﬁnite for every i. Then the ﬁrst non”
Cofiniteness of local cohomology modules for ideals of small dimension (2009, background): “(As in [9], an R-module M is called weakly Laskerian if the set of associated primes of any quotient module M is finite.”
ON GENERALIZED REGULAR SEQUENCES AND THE FINITENESS FOR ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES (2005, background): “It has shown by Khashyarmanesh and Salarian ( 1999 ) that if i is an integer such that Supp <inline-graphic xmlns:xlink="http://www.”
Local cohomology and Serre subcategories (2008, unknown): “Moreover the ﬁniteness of Ass R ( H n (M)) under the assumption in (c) has been proved in [14, Theorem B( β )] and [2, Theorem 2.3] for ﬁnite modules and in [10, Corollary 2.7] for weakly Laskerian modules.”
Associated Primes of Local Cohomology Modules of Weakly Laskerian Modules (2005, background): “It is known that if either M is reflexive or linearly compact, then M has a finitely generated submodule S such that M/S is Artinian (see e.g., Divaani-Aazar and Mafi, 2005, Example 2.2).”