Results on Graded Generalized Local Cohomology

Abstract

Let R = ⨁ _i≥0 R _i be a positively graded Noetherian ring with irrelevant ideal R ₊ = ⨁ _i≥1 R _i , and let M, N be two finitely generated graded R-modules such that pd(M) is finite. We show that the least integer i for which is not asymptotically zero is equal to the least integer i such that . Also, whenever R is homogeneous with local base ring (R ₀, 𝔪₀), we prove some Artinian and tameness property for .

Key Words:

• Generalized local cohomology
• Graded rings and modules

2000 Mathematics Subject Classification:

• Primary 13D45, 13E10

ACKNOWLEDGMENT

The author is grateful to the referee for his/her careful reading of the manuscript and useful suggestions.

Notes

Communicated by A. K. Singh.