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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.
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Takagi Station (高木駅, Takagi-eki) is a train station in Fuchū, Hiroshima Prefecture, Japan.
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