Annihilator of Top Local Cohomology and Lynch's Conjecture

Abstract

Let R be a commutative Noetherian ring, a a proper ideal of R and N a nonzero finitely generated R-module with N = aN . Let c be the greatest nonnegative integer i such that the local cohomology H i a (N ) is nonzero. In this paper, we provide a sharp bound under inclusion for the annihilator of the top local cohomology module H c a (N ) and this annihilator is computed in certain cases. Also, using this bound, we construct a counterexample to Lynch's conjecture.