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By Takagi S.

We introduce a brand new variation of tight closure and provides an interpretation of adjoint beliefs through this tight closure. As a corollary, we end up log pair (X, Δ) is plt if and provided that the modulo p aid of (X, Δ) is divisorially F-regular for all huge p ≫ zero. the following, divisorially F-regular pairs are a category of singularities in confident attribute brought via Hara and Watanabe (J Algebra Geom 11:363-392, 2002) when it comes to Frobenius splitting.

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