A Property of the Frobenius Map of a Polynomial Ring
Abstract
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 R be the Frobenius map of R, i.e. F(r)=rp. We explicitly describe an R-module isomorphism HomR(F*(M),N) HomR(M,F*(N)) for all R-modules M and N. Some recent and potential applications are discussed.
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