A Property of the Frobenius Map of a Polynomial Ring

Details A Property of the Frobenius Map of a Polynomial Ring A Property of the Frobenius Map of a Polynomial Ring

2010-01-18

arxiv.org/abs/1001.2949v1

Mathematics

Commutative Algebra

7 pages

Scientific paper

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.

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