On the interplay between the Frobenius functor and its dual

摘要

For a commutative Noetherian ring R of prime characteristic, denote by R-f the ring R with the left structure given by the Frobenius map. We develop Thomas Marley's work on the property of the Frobenius functor F(-) = -circle times R-f(R) and show some interplays between F and its dual (F) over tilde(-) = Hom (R)(R-f-), which is introduced by Jurgen Herzog.