A Finiteness Result for Co-Associated and Associated Primes of Generalized Local Homology and Cohomology Modules

Abstract

We show that if M is a finitely generated R-module, N is an I-stable semi-discrete linearly compact R-module and G is a closed R-submodule of the generalized local homology module such that is I-stable for all j < i and is I-stable, then the set Coass G is finite. As an immediate consequence, the first non-I-stable generalized local homology module of N, M with respect to I has only finitely many co-associated primes. By duality, we get a new result for the finiteness of associated primes of (generalized) local cohomology modules.