Nash blowups in prime characteristic (Q832442)

Summary: We initiate the study of Nash blowups in prime characteristic. First, we show that a normal variety is non-singular if and only if its Nash blowup is an isomorphism, extending a theorem by \textit{A. Nobile} [Pac. J. Math. 60, No. 1, 297--305 (1975; Zbl 0324.32012)]. We also study higher Nash blowups, as defined by T. Yasuda. Specifically, we give a characteristic-free proof of a higher version of Nobile's theorem for quotient varieties and hypersurfaces. We also prove a weaker version for \(F\)-pure varieties.