2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129068We 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 $p \gg 0$. 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 fixedAlgebraic GeometryCommutative Algebra14B05 (Primary); 13A35 (Secondary)text