ON GRADED LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS

Let R = ? n2N0 Rn be a standard graded ring, M be a nitely-generated graded R-module, and J be a homogeneous ideal of R. In this work, we study the graded structure of the i-th local cohomology module of M, dened by a pair of ideals (R+; J), i.e. HiR +;J (M). More precisely, we discuss the niteness property and vanishing of the graded components HiR +;J (M)n. Also, we study the Artinian property and tameness of certain submodules and quotient modules of HiR +;J (M).