Symbolic powers, integral closure and local cohomology

Abstract

Let Ibe an ideal of a Noetherian ring Rand let S be a multiplicatively closed subset of R. The purpose of this paper is to compare the topologies defined by the integral filtration {Īⁿ}_n≥0 and the (S)-symbolic filtration {S(Iⁿ)}_n≥0 using the natural homomorphisms between the local cohomology groups {H⁰ _q(R÷Iⁿ)}_n≥0 and {H⁰ _q(R÷Īⁿ)}_n≥0.