\(F\)-regularity and \(F\)-purity of graded rings
For a Noetherian ring \(R\) of characteristic \(p > 0\), the notions of \(F\)-purity and \(F\)-regularity are defined using the Frobenius action on \(R\) and the notion of tight closure. This paper gives several necessary and sufficient conditions for a normal graded ring \(R = R(X,D)\) to be either \(F\)-regular or \(F\)-pure, where \(X = \text{Proj} (R)\) is a normal complete intersection subvariety of projective space over a perfect field \(k\) of characteristic \(p > 0\) and \(D\) is a rational coefficient divisor on \(X\).
scientific article; zbMATH DE number 763929