On the Vanishing and the Finiteness of Supports of Generalized Local Cohomology Modules

2007/05/31 by Cuong, Nguyen Tu, Van Hoang, Nguyen
#13C15 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0705.4553

Abstract

Let (R,\fr m) be a Noetherian local ring, I an ideal of R and M, N two finitely generated R-modules. The first result of this paper is to prove a vanishing theorem for generalized local cohomology modules which says that H^j_I(M,N)=0 for all j>dim(R), provided M is of finite projective dimension. Next, we study and give characterizations for the least and the last integer r such that \Supp(H^r_I(M,N)) is infinite.

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