Cofiniteness and associated primes of local cohomology modules

By T. Marley, J. Vassilev. 2002

90 citations recorded by the source corpus.

Abstract Let R be a d -dimensional regular local ring, I an ideal of R , and M a finitely generated R -module of dimension n . We prove that the set of associated primes of Ext R i (R/I,H I j (M)) is finite for all i and j in the following cases: (a)  dim M⩽3 ; (b)  dim R⩽4 ; (c)  dim M/IM⩽2 and M satisfies Serre's condition S n−3 ; (d)  dim M/IM⩽3 , ann R M=0 , R is unramified, and M satisfies S n−3 . In these cases we also prove that H I i (M) p is I p -cofinite for all but finitely many primes p of R . Additionally, we show that if dim R/I⩾2 and Spec R/I−{m/I} is disconnected then H I d−1 (R) is not I -cofinite, generalizing a result due to Huneke and Koh.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/64b6e74fb1fbc88d7db747153874cc2e8a8f3ff4

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In Algebra and Number Theory

1. K. Divaani-Aazar
2. A. Mafi
3. Irena Swanson
4. Anurag Singh
5. M. Dibaei
6. Siamak Yassemi
7. Le Thanh Nhan

In Geometry and Topology

1. K. Divaani-Aazar
2. A. Mafi
3. Irena Swanson
4. Anurag Singh
5. M. Dibaei
6. Siamak Yassemi
7. Le Thanh Nhan

Citations in the corpus

• Associated Primes of Local Cohomology Modules of Weakly Laskerian Modules (2005, background): “But H 2 a (R) is a-weakly cofinite, by Corollary 3.4 i). ii) Let R and a be either as in Example 3.7 or as in Example 3.10 in [ 12 ].”
• Associated primes of local cohomology modules and of Frobenius powers (2004, background): “For some of the other work on this question, we refer the reader to [4, 5, 8, 22, 25, 32].”