J. Aust. Math. Soc. 83 (2007), no. 2, pp. 217–225.

On the asymptotic behaviour of associated primes of generalized local cohomology modules

Kazem Khashyarmanesh Ahmad Abbasi
Fedowsi University of Mashhad
Department of Mathematics
P.O. Box 1159-91775
Mashhad
Iran

and

Institute for Studies in Theoretical Physics and Mathematics
P.O. Box 19395-5746
Tehran
Iran
khashyar@ipm.ir
Guilan University
Department of Mathematics
P.O. Box 41335-1914
Rasht
Iran
aabbasi@guilan.ac.ir
Received 15 November 2004; revised 24 July 2006
Communicated by J. Du

Abstract

Let M and N be finitely generated and graded modules over a standard positive graded commutative Noetherian ring R, with irrelevant ideal R_+. Let H^k_{R_+}(M,N)_n be the nth component of the graded generalized local cohomology module H^k_{R_+}(M,N). In this paper we study the asymptotic behaviour of \operatorname {Ass}_{R_+}\big (H^k_{R_+}(M,N)_n\big ) as n\to -\infty whenever k is the least integer j for which the ordinary local cohomology module H^j_{R_+}(N) is not finitely generated.

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2000 Mathematics Subject Classification: primary 13D45, 13A02, 13E05; secondary 14B15
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