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.

21 pages in AMS LaTeX, to appear in Journal of Algebraic Geometry