ANNIHILATORS OF TOP LOCAL COHOMOLOGY

In many important theorems in the homological theory of commutative local rings, an essential ingredient in the proof is to consider Ann(R)H(I)(i)(R). We examine these annihilators for an arbitrary local ring when i is the cohomological dimension of I. When the cohomological dimension coincides with the dimension of the ring, we provide an explicit description of Ann(R)H(I)(i)(R). In general, we examine its dimension over R and conjecture that dim R/Ann(R)H(I)(i)(R) = dim R/H-I(0)(R) for i > 0