Graded local cohomology modules with respect to the linked ideals

Abstract

Let R = ⊕ n∈N0 R n be a standard graded ring, M be a finitely generated graded R-module and R + := ⊕ n∈N R n denotes the irrelevant ideal of R. In this paper, considering the new concept of linkage of ideals over a module, we study the graded components H i a (M ) n when a is an h-linked ideal over M . More precisely, we show that H i a (M ) is tame in each of the following cases:(i) i = f R+ a (M ), the first integer i for which R + 0 : H i a (M ); (ii) i = cd(R + , M ), the last integer i for which H i R+ (M ) = 0, and a = b + R + where b is an h-linked ideal with R + over M . Also, among other things, we describe the components H i a (M ) n where a is radically h-Mlicci with respect to R + of length 2.