This paper presents three results on -singularities. First, we give a new proof of Eisenstein’s restriction theorem for adjoint ideal sheaves using the theory of -singularities. Second, we show that a conjecture of Mustaţă and Srinivas implies a conjectural correspondence of -purity and log canonicity. Finally, we prove this correspondence when the defining equations of the variety are very general.
Shunsuke Takagi. "Adjoint ideals and a correspondence between log canonicity and $F$-purity." Algebra Number Theory 7 (4) 917 - 942, 2013. https://doi.org/10.2140/ant.2013.7.917