On The Matlis Duals Of Local Cohomology Modules

Abstract

Let (R, m) be a Noetherian regular local ring of characteristic p > 0 and let I be a nonzero ideal of R. Let D(-) = Hom(R)(-, E) be the Matlis dual functor, where E = E-R(R/m) is the injective hull of the residue field R/m. In this short note, we prove that if H-I(i) (R) not equal 0, then Supp(R)(D(H-I(i) (R))) = Spec(R).