COHOMOLOGICAL DIMENSION FILTRATION AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES

Let a denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration M = {M-i}(i-0)(c) , where c = cd (a, M) and M-i denotes the largest submodule of M such that cd (a, M-i) <= i . Some properties of this filtration are investigated. In particular, if (R, m) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module H-a(c) (M), namely Ann(R) (H-a(c) (M)) - Ann(R) (M/Mc-1). As a consequence, there exists an ideal b of R such that Ann(R) (H-a(c) (M)) = Ann(R) (M/H-b(0) (M)). This generalizes the main results of Bahmanpour et al. (2012) and Lynch (2012).