A characteristic <Emphasis Type="Italic">p</Emphasis> analogue of plt singularities and adjoint ideals

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, Δ) is plt if and only if the modulo p reduction of (X, Δ) is divisorially F-regular for all large p ≫ 0. Here, divisorially F-regular pairs are a class of singularities in positive characteristic introduced by Hara and Watanabe (J Algebra Geom 11:363–392, 2002) in terms of Frobenius splitting. The author was partially supported by Grant-in-Aid for Young Scientists (B) 17740021 from JSPS.