Let R be a ring of polynomials in a finite number of variables over a perfect
field k of characteristic p>0 and let F:R\to R be the Frobenius map of R, i.e.
F(r)=r^p. We explicitly describe an R-module isomorphism Hom_R(F_*(M),N)\cong
Hom_R(M,F^*(N)) for all R-modules M and N. Some recent and potential
applications are discussed.