A characteristic p analogue of plt singularities and adjoint ideals

Abstract

We introduce a new variant of tight closure and give an interpretation of adjoint ideals via this tight closure. As a corollary, we prove that a log pair $(X,\Delta )$ is plt if and only if the modulo $p$ reduction of $(X,\Delta )$ is divisorially F-regular for all large $p\gg 0$. Here, divisorially F-regular pairs are a class of singularities in positive characteristic introduced by Hara and Watanabe in terms of Frobenius splitting.

22 pages. A lot of changes. Some errors and many typos fixed