  This paper investigates when local cohomology modules have an annihilator
that does not depend on the choice of an ideal. Takahashi classified the
dominant resolving subcategories of the category of finitely generated modules
over a commutative Noetherian ring. We show that his classification theorem
describes annihilation results of local cohomology modules over a
finite-dimensional ring with certain assumptions or a Cohen-Macaulay ring.
