Annihilator of top local cohomology and Lynch’s conjecture

Abstract

Let [Formula: see text] be a commutative Noetherian ring, [Formula: see text] a proper ideal of [Formula: see text] and [Formula: see text] a nonzero finitely generated [Formula: see text]-module with [Formula: see text]. Let [Formula: see text] (respectively, [Formula: see text]) be the smallest (respectively, greatest) non-negative integer [Formula: see text] such that the local cohomology [Formula: see text] is nonzero. In this paper, we provide sharp bounds under inclusion for the annihilators of the local cohomology modules [Formula: see text], [Formula: see text] and these annihilators are computed in certain cases. Also, we construct a counterexample to Lynch’s conjecture.