An interpretation of multiplier ideals via tight closure

Abstract

Hara [Ha3] and Smith [Sm2] independently proved that in a normal Q-Gorenstein ring of characteristic p 0, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair (R,∆) of a normal ring R and an effective Q-Weil divisor ∆ on SpecR. As a corollary, we obtain the equivalence of strongly F-regular pairs and klt pairs.