On the Hartshorne--Speiser--Lyubeznik Theorem about Artinian modules with a Frobenius action

2006/05/12 by Rodney Y. Sharp, Sharp, Rodney Y.
Mathematics · #13A35 #13E10 #16S36 (Primary) 13D45 (Secondary) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13A35 #msc:13D45 #msc:13E10 #msc:16S36

paper · pdf · doi:10.48550/arxiv.math/0605330

This is to appear in the Proceedings of the American Mathematical Society

arxiv created 2006/05/12 · openalex publication_date 2006/05/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring R[x,f] (associated to R and the Frobenius homomorphism f, in the indeterminate x) that is both x-torsion and Artinian over R.

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