SYMBOLIC POWERS, INTEGRAL CLOSURE AND LOCAL COHOMOLOGY

Let I be an ideal of a Noetherian ring R and let S be a multiplicative ly closed subset of R. The purpose of this paper is to compare the top ologies defined by the integral filtration {($) over bar I-$ over bar n}(n greater than or equal to 0) and the (S)-symbolic filtration {S(I- n)}(n greater than or equal to 0) using the natural homomorphisms betw een tile local cohomology groups {($) over bar H-q(0)(R/I-n)}(n greate r than or equal to 0) and {H-q(0)(R/($) over bar I-$ over bar n)}(n gr eater than or equal to 0).