An interpretation of multiplier ideals via tight closure

Abstract

Hara and Smith independently proved that in a normal $\mQ$-Gorenstein ring of characteristic $p \gg 0$, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair $(R, \Delta)$ of a normal ring $R$ and an effective $\mQ$-Weil divisor $\Delta$ on $\Spec R$. As a corollary, we obtain the equivalence of strongly F-regular pairs and klt pairs.