A Property of the Frobenius Map of a Polynomial Ring

2010/01/18 by Gennady Lyubeznik, Lyubeznik, Gennady, Wenliang Zhang +3
Computer Science · Mathematics · #13A35 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13A35

paper · pdf · doi:10.48550/arxiv.1001.2949

7 pages

arxiv created 2010/01/18 · openalex publication_date 2010/01/18 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)=r^p. We explicitly describe an R-module isomorphism Hom_R(F_*(M),N)≅ Hom_R(M,F^*(N)) for all R-modules M and N. Some recent and potential applications are discussed.

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