부산대학교 도서관

The study of Frobenius actions on local cohomology modules over a local ring of prime characteristic has interesting connections with the theory of tight closure. This paper establishes new connections by developing the notion of relative Frobenius actions on local cohomology. As an application, we show that a ring has $F$-nilpotent singularities if and only if the tight closure of every parameter ideal is equal to its Frobenius closure.
Comment: Final version, to appear in Journal of Algebra